Quadratic Function — Standard Form (Basic)

Quadratic Function — Standard Form (Basic). Practice questions to deepen understanding of the standard form of a quadratic function. Online math practice with full solutions and step-by-step explanations.

Quadratic Function — Standard Form Basic — convert from general form to standard form, find the vertex, axis of symmetry, and opening direction. Visual explanations with worked examples.

50 questions

Question 1

2.00 pts

In the function \(y = 2x^2 + 3x + 5\), what is the coefficient \(a\)?

\(a = 2\)

\(a = 3\)

\(a = 5\)

\(a = 1\)

Explanation:

Standard form: (y = ax^2 + bx + c). The coefficient (a) is the coefficient of (x^2). In the equation (y = 2x^2 + 3x + 5): (a = 2).

Question 2

2.00 pts

In the function \(y = -x^2 + 4x - 1\), what is the coefficient \(a\)?

\(a = -1\)

\(a = 1\)

\(a = 4\)

\(a = -4\)

Explanation:

In the equation (y = -x^2 + 4x - 1): the coefficient of (x^2) is (-1), therefore (a = -1).

Question 3

2.00 pts

In the function \(y = 5x^2 - 2x + 1\), what is the coefficient \(a\)?

\(a = 5\)

\(a = -2\)

\(a = 1\)

\(a = -5\)

Explanation:

The coefficient of (x^2) is (5), therefore (a = 5).

Question 4

2.00 pts

In the function \(y = -3x^2 + x - 7\), what is the coefficient \(a\)?

\(a = -3\)

\(a = 3\)

\(a = 1\)

\(a = -7\)

Explanation:

The coefficient of (x^2) is (-3), therefore (a = -3).

Question 5

2.00 pts

In the function \(y = x^2 + 6x - 4\), what is the coefficient \(a\)?

\(a = 1\)

\(a = 6\)

\(a = -4\)

\(a = 0\)

Explanation:

When no coefficient is written before (x^2), the coefficient is (1). Therefore (a = 1).

Question 6

2.00 pts

In the function \(y = 0.5x^2 + 2x\), what is the coefficient \(a\)?

\(a = 0.5\)

\(a = 2\)

\(a = 1\)

\(a = 0\)

Explanation:

The coefficient of (x^2) is (0.5), therefore (a = 0.5).

Question 7

2.00 pts

In the function \(y = -4x^2 - 5x + 2\), what is the coefficient \(a\)?

\(a = -4\)

\(a = 4\)

\(a = -5\)

\(a = 2\)

Explanation:

The coefficient of (x^2) is (-4), therefore (a = -4).

Question 8

2.00 pts

In the function \(y = 10x^2\), what is the coefficient \(a\)?

\(a = 10\)

\(a = 0\)

\(a = 1\)

\(a = 2\)

Explanation:

The coefficient of (x^2) is (10), therefore (a = 10).

Question 9

2.00 pts

In the function \(y = -0.2x^2 + 3x - 1\), what is the coefficient \(a\)?

\(a = -0.2\)

\(a = 0.2\)

\(a = 3\)

\(a = -1\)

Explanation:

The coefficient of (x^2) is (-0.2), therefore (a = -0.2).

Question 10

2.00 pts

In the function \(y = 7x^2 + x\), what is the coefficient \(a\)?

\(a = 7\)

\(a = 1\)

\(a = 0\)

\(a = 8\)

Explanation:

The coefficient of (x^2) is (7), therefore (a = 7).

Question 11

2.00 pts

In the function \(y = 3x^2 - 7x + 2\), what is the coefficient \(b\)?

\(b = -7\)

\(b = 7\)

\(b = 3\)

\(b = 2\)

Explanation:

The coefficient (b) is the coefficient of (x). (b = -7).

Question 12

2.00 pts

In the function \(y = x^2 + 5x - 3\), what is the coefficient \(b\)?

\(b = 5\)

\(b = 1\)

\(b = -3\)

\(b = -5\)

Explanation:

The coefficient of (x) is (5).

Question 13

2.00 pts

In the function \(y = -2x^2 + x + 8\), what is the coefficient \(b\)?

\(b = 1\)

\(b = -2\)

\(b = 8\)

\(b = -1\)

Explanation:

The coefficient of (x) is (1).

Question 14

2.00 pts

In the function \(y = 4x^2 - 3\), what is the coefficient \(b\)?

\(b = 0\)

\(b = 4\)

\(b = -3\)

\(b = 1\)

Explanation:

There is no term with (x), therefore (b = 0).

Question 15

2.00 pts

In the function \(y = 2x^2 - x + 5\), what is the coefficient \(b\)?

\(b = -1\)

\(b = 1\)

\(b = 2\)

\(b = 5\)

Explanation:

The coefficient of (x) is (-1).

Question 16

2.00 pts

In the function \(y = -x^2 - 6x + 1\), what is the coefficient \(b\)?

\(b = -6\)

\(b = 6\)

\(b = -1\)

\(b = 1\)

Explanation:

The coefficient of (x) is (-6).

Question 17

2.00 pts

In the function \(y = 5x^2 + 10x\), what is the coefficient \(b\)?

\(b = 10\)

\(b = 5\)

\(b = 0\)

\(b = 15\)

Explanation:

The coefficient of (x) is (10).

Question 18

2.00 pts

In the function \(y = -3x^2 + 0.5x - 2\), what is the coefficient \(b\)?

\(b = 0.5\)

\(b = -0.5\)

\(b = -3\)

\(b = -2\)

Explanation:

The coefficient of (x) is (0.5).

Question 19

2.00 pts

In the function \(y = x^2 - 4x + 3\), what is the coefficient \(b\)?

\(b = -4\)

\(b = 4\)

\(b = 3\)

\(b = 1\)

Explanation:

The coefficient of (x) is (-4).

Question 20

2.00 pts

In the function \(y = 6x^2 + 2x - 1\), what is the coefficient \(b\)?

\(b = 2\)

\(b = 6\)

\(b = -1\)

\(b = 8\)

Explanation:

The coefficient of (x) is (2).

Question 21

2.00 pts

In the function \(y = x^2 + 3x - 2\), what is the coefficient \(c\)?

\(c = -2\)

\(c = 2\)

\(c = 3\)

\(c = 1\)

Explanation:

The coefficient (c) is the constant term. (c = -2).

Question 22

2.00 pts

In the function \(y = 2x^2 - 4x + 7\), what is the coefficient \(c\)?

\(c = 7\)

\(c = -4\)

\(c = 2\)

\(c = -7\)

Explanation:

The constant term is (7).

Question 23

2.00 pts

In the function \(y = -x^2 + 5x\), what is the coefficient \(c\)?

\(c = 0\)

\(c = 5\)

\(c = -1\)

\(c = 1\)

Explanation:

There is no constant term, therefore (c = 0).

Question 24

2.00 pts

In the function \(y = 3x^2 - x + 10\), what is the coefficient \(c\)?

\(c = 10\)

\(c = 3\)

\(c = -1\)

\(c = -10\)

Explanation:

The constant term is (10).

Question 25

2.00 pts

In the function \(y = -2x^2 + 4x - 5\), what is the coefficient \(c\)?

\(c = -5\)

\(c = 5\)

\(c = 4\)

\(c = -2\)

Explanation:

The constant term is (-5).

Question 26

2.00 pts

In the function \(y = x^2 + 8\), what is the coefficient \(c\)?

\(c = 8\)

\(c = 1\)

\(c = 0\)

\(c = -8\)

Explanation:

The constant term is (8).

Question 27

2.00 pts

In the function \(y = 4x^2 - 3x - 6\), what is the coefficient \(c\)?

\(c = -6\)

\(c = 6\)

\(c = -3\)

\(c = 4\)

Explanation:

The constant term is (-6).

Question 28

2.00 pts

In the function \(y = -5x^2 + 2x + 1\), what is the coefficient \(c\)?

\(c = 1\)

\(c = 2\)

\(c = -5\)

\(c = -1\)

Explanation:

The constant term is (1).

Question 29

2.00 pts

In the function \(y = 0.5x^2 - 3x + 4.5\), what is the coefficient \(c\)?

\(c = 4.5\)

\(c = 0.5\)

\(c = -3\)

\(c = -4.5\)

Explanation:

The constant term is (4.5).

Question 30

2.00 pts

In the function \(y = 7x^2 - 2x\), what is the coefficient \(c\)?

\(c = 0\)

\(c = 7\)

\(c = -2\)

\(c = 1\)

Explanation:

There is no constant term, therefore (c = 0).

Question 31

2.00 pts

Does the parabola \(y = 3x^2 - 2x + 1\) open upward or downward?

Opens upward ↑

Opens downward ↓

straight line

No parabola

Explanation:

The coefficient (a = 3 > 0). When (a > 0), the parabola opens upward.

Question 32

2.00 pts

Does the parabola \(y = -2x^2 + 5x - 1\) open upward or downward?

Opens downward ↓

Opens upward ↑

straight line

No parabola

Explanation:

The coefficient (a = -2 < 0). When (a < 0), the parabola opens downward.

Question 33

2.00 pts

What is the y-intercept of the function \(y = x^2 + 3x + 5\)?

\((0, 5)\)

\((5, 0)\)

\((0, 3)\)

\((3, 0)\)

Explanation:

The intersection point is: ((0, c) = (0, 5)).

Question 34

2.00 pts

What is the y-intercept of the function \(y = 2x^2 - 3x - 4\)?

\((0, -4)\)

\((-4, 0)\)

\((0, 2)\)

\((0, -3)\)

Explanation:

The intersection point is: ((0, -4)).

Question 35

2.00 pts

What is the y-intercept of the function \(y = -x^2 + 4x\)?

\((0, 0)\)

\((0, 4)\)

\((4, 0)\)

\((0, -1)\)

Explanation:

There is no constant term, therefore (c = 0). Intersection point: ((0, 0)).

Question 36

2.00 pts

In the function \(y = -5x^2 + 2x + 3\), what are \(a, b, c\)?

\(a = -5, b = 2, c = 3\)

\(a = 5, b = 2, c = 3\)

\(a = -5, b = -2, c = 3\)

\(a = -5, b = 2, c = -3\)

Explanation:

(a = -5, b = 2, c = 3).

Question 37

2.00 pts

Which of the functions intersects the y-axis at \((0, 7)\)?

\(y = 3x^2 - x + 7\)

\(y = 7x^2 - x + 3\)

\(y = 3x^2 - x - 7\)

\(y = x^2 + 7x + 3\)

Explanation:

The intersection point is ((0, c)). If ((0, 7)), then (c = 7).

Question 38

2.00 pts

In the function \(y = x^2 - 6x + 5\), what is the function value when \(x = 0\)?

\(y = 5\)

\(y = -6\)

\(y = 1\)

\(y = 0\)

Explanation:

When (x = 0): (y = 5). This is also c.

Question 39

2.00 pts

Which of the parabolas opens downward?

\(y = -4x^2 + 3x - 2\)

\(y = 4x^2 + 3x - 2\)

\(y = x^2 - 3x + 2\)

\(y = 0.5x^2 + x - 1\)

Explanation:

A downward-opening parabola → (a < 0). Only (a = -4).

Question 40

2.00 pts

In the function \(y = 2x^2 + 5x - 3\), what is the function value when \(x = 1\)?

\(y = 4\)

\(y = 7\)

\(y = -3\)

\(y = 10\)

Explanation:

Substitute (x = 1): (y = 2 + 5 - 3 = 4).

Question 41

2.00 pts

According to the graph, does the parabola open upward or downward? What is the sign of \(a\)?

Opens upward, \(a > 0\)

Opens downward, \(a < 0\)

Opens upward, \(a < 0\)

Opens downward, \(a > 0\)

Explanation:

The parabola opens upward → opens upward. Therefore (a > 0).

Question 42

2.00 pts

According to the graph, does the parabola open upward or downward?

Opens downward, \(a < 0\)

Opens upward, \(a > 0\)

Opens downward, \(a > 0\)

Opens upward, \(a < 0\)

Explanation:

The parabola opens downward → opens downward. Therefore (a < 0).

Question 43

2.00 pts

According to the graph, what is the coefficient \(a\)?

\(a > 0\)

\(a < 0\)

\(a = 0\)

Cannot be determined

Explanation:

The parabola opens upward, therefore (a > 0).

Question 44

2.00 pts

According to the graph, what is the coefficient \(a\)?

\(a < 0\)

\(a > 0\)

\(a = 0\)

Cannot be determined

Explanation:

The parabola opens downward, therefore (a < 0).

Question 45

2.00 pts

According to the graph, which equation fits?

\(y = 2x^2 + 3x + 1\)

\(y = -2x^2 + 3x + 1\)

\(y = -x^2 - 3x - 1\)

\(y = -5x^2 + 2x - 1\)

Explanation:

The parabola opens upward → (a > 0). Only (y = 2x^2 + 3x + 1).

Question 46

2.00 pts

According to the graph, which equation fits?

\(y = -3x^2 + 4x - 1\)

\(y = 3x^2 + 4x - 1\)

\(y = x^2 - 4x + 1\)

\(y = 5x^2 - 2x + 3\)

Explanation:

The parabola opens downward → (a < 0). Only (y = -3x^2 + 4x - 1).

Question 47

2.00 pts

According to the graph, what is the y-intercept?

\((0, 3)\)

\((3, 0)\)

\((0, 0)\)

\((0, -3)\)

Explanation:

The marked point: ((0, 3)).

Question 48

2.00 pts

According to the graph, does the parabola open upward or downward?

Opens upward ↑

Opens downward ↓

straight line

Cannot be determined

Explanation:

The parabola opens upward → opens upward.

Question 49

2.00 pts

According to the graph, does the parabola open upward or downward?

Opens downward ↓

Opens upward ↑

straight line

Cannot be determined

Explanation:

The parabola opens downward → opens downward.

Question 50

2.00 pts

According to the graph, what is the sign of \(a\) and does the parabola open upward or downward?

\(a > 0\), opens upward

\(a < 0\), opens downward

\(a > 0\), opens downward

\(a < 0\), opens upward

Explanation:

The parabola opens upward, therefore (a > 0) and the parabola opens upward.