Quiz about Quadratic Functions Mastery Quiz

Question 1

Solve the quadratic equation $$x^2 - 5x + 6 = 0$$ algebraically.

Accepted Answer

$$x = 2$$ and $$x = 3$$

Answer

$$x = 1$$ and $$x = 6$$

Answer

$$x = -2$$ and $$x = -3$$

Answer

$$x = 0$$

Question 2

Determine the direction of opening for the quadratic function $$f(x) = -2x^2 + 4x - 1$$ .

Accepted Answer

Opens downwards

Answer

Opens upwards

Answer

Opens to the right

Answer

Opens to the left

Question 3

Graph the quadratic function $$y = x^2 - 4x + 4$$ . What is the vertex of this parabola?

Accepted Answer

$$(2, 4)$$

Answer

$$(2, 0)$$

Answer

$$(0, 4)$$

Answer

$$(2, -4)$$

Question 4

Which of the following represents a quadratic function in standard form?

Accepted Answer

$$y = 2x^2 - 6x + 5$$

Answer

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

Answer

$$y = x(x - 5)$$

Answer

$$y = \frac{1}{2}x + 3$$

Question 5

Given the quadratic equation $$3x^2 - 12x + 9 = 0$$ , solve for $$x$$ .

Accepted Answer

$$x = 1$$

Answer

$$x = 1$$ and $$x = 3$$

Answer

$$x = 2$$

Answer

$$x = 0$$

Question 6

What is the axis of symmetry for the quadratic function $$f(x) = -x^2 + 6x - 8$$ ?

Accepted Answer

$$x = 3$$

Answer

$$x = -3$$

Answer

$$x = 6$$

Answer

$$x = -6$$

Question 7

For the quadratic function $$y = 4x^2 - 16x + 15$$ , what are the x-intercepts?

Accepted Answer

$$x = 1.5$$ and $$x = 2.5$$

Answer

$$x = 3$$ and $$x = 5$$

Answer

$$x = 1$$ and $$x = 3.75$$

Answer

No real x-intercepts

Question 8

Graph the quadratic function $$y = -3x^2 + 6x - 2$$ . What is the y-intercept of this parabola?

Accepted Answer

$$-2$$

Answer

$$2$$

Answer

$$-3$$

Answer

$$3$$

Question 9

Which of the following quadratic functions has its vertex in the second quadrant?

Accepted Answer

$$y = -x^2 - 6x - 9$$

Answer

$$y = x^2 + 4x + 1$$

Answer

$$y = x^2 - 8x + 16$$

Answer

$$y = -x^2 + 2x - 3$$

Question 10

If the quadratic function $$f(x) = ax^2 + bx + c$$ opens upwards, which of the following must be true?

Accepted Answer

$$a > 0$$

Answer

$$a < 0$$

Answer

$$b > 0$$

Answer

$$c > 0$$

Question 11

Solve the quadratic equation $$2x^2 - 4x - 6 = 0$$ using the quadratic formula.

Accepted Answer

$$x = 3$$ and $$x = -1$$

Answer

$$x = -1$$ and $$x = 3$$

Answer

$$x = 1$$ and $$x = -3$$

Answer

$$x = -3$$ and $$x = 1$$

Question 12

What is the minimum value of the quadratic function $$f(x) = 2x^2 - 8x + 6$$ ?

Accepted Answer

$$-2$$

Answer

$$2$$

Answer

$$-4$$

Answer

$$4$$

Question 13

For the quadratic function $$y = -x^2 + 4x - 3$$ , what is the maximum value?

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$4$$

Answer

$$-3$$

Question 14

Given the quadratic function in standard form $$f(x) = 5x^2 - 20x + 15$$ , factor it completely.

Accepted Answer

$$5(x - 2)^2$$

Answer

$$5(x - 3)(x - 5)$$

Answer

$$5(x - 1)(x - 3)$$

Answer

Cannot be factored

Question 15

Which of the following is the correct graph for the quadratic equation $$y = x^2 - 2x - 3$$ ?

Accepted Answer

Vertex at $$(1, -4)$$ , opens upwards

Answer

Vertex at $$(-1, -4)$$ , opens downwards

Answer

Vertex at $$(1, -4)$$ , opens downwards

Answer

Vertex at $$(-1, 4)$$ , opens upwards

Question 16

A parabola reflects over?

Accepted Answer

the axis of symmetry

Answer

the y-intercept

Answer

the maximum

Answer

the minimum

Question 17

A maximum is the _____________ point of the function.

Accepted Answer

highest

Answer

lowest

Question 18

A minimum is the ______________ point of the function.

Accepted Answer

lowest

Answer

highest

Question 19

The constant term of a quadratic function is the...?

Accepted Answer

y-intercept

Answer

vertex

Answer

minimum

Answer

axis of symmetry

Quadratic Functions Mastery Quiz

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