Q: Find the $$x-$$intercepts of $$y = x^2$ - 4x - 9$$ using the quadratic formula.

$$x = 2 + \\sqrt{13}$$ and $$x = 2 - \\sqrt{13}$$

Q: Given $$y = 3(x-2)^2$ - 6$$, what is the domain and range of the function?

Domain: $$(-\\infty, \\infty)$$, Range: $$[-6, \\infty)$$

Q: Solve the quadratic inequality $$x^2 - 3x - 4$$ \u003e 0$$.

$$(-\\infty, -1) \\cup (4, \\infty)$$

Q: Which of the following is the correct factorization of $$x^2 - 4x - 9$?

$$(x - (2 + \\sqrt{13}))(x - (2 - \\sqrt{13}))$$

Question 1

Given the quadratic function $$y = 2x^2$ - 4x + 3$$, rewrite it in vertex form.

Accepted Answer

$$y = 2(x-1)^2$ + 1$$

Question 2

What is the vertex of the parabola $$y = -rac{1}{2}x^2$ + 8$$?

Accepted Answer

$$(0, 8)$$

Question 3

For the quadratic function $$y = a(x-h)^2$ + k$$, which statement is true about the axis of symmetry?

Accepted Answer

It is the vertical line $$x = h$$

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 5

Which of the following describes the graph of $$y = -2(x+3)^2$ + 5$$?

Accepted Answer

Opens downward, vertex at $$(-3, 5)$$

Question 6

Find the $$x-$$intercepts of $$y = x^2$ - 4x - 9$$ using the quadratic formula.

Accepted Answer

$$x = 2 + \sqrt{13}$$ and $$x = 2 - \sqrt{13}$$

Question 7

Given $$y = 3(x-2)^2$ - 6$$, what is the domain and range of the function?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-6, \infty)$$

Question 8

If $$y = x^2$ + 6x + 9$$, which transformation has occurred compared to $$y = x^2$?

Accepted Answer

Shift left 3 units

Question 9

Solve the quadratic inequality $$x^2 - 3x - 4$$ \u003e 0$$.

Accepted Answer

$$(-\infty, -1) \cup (4, \infty)$$

Question 10

Using synthetic division, what is the remainder when $$x^3$$ - $$5x^2 + 6x$ is divided by x - 3$?

Accepted Answer

$$0$$

Question 11

For the quadratic $$y = -rac{1}{2}x^2$ + 8$$, what is the interval on which the function is increasing?

Accepted Answer

$$(-\infty, 0)$$

Question 12

What is the axis of symmetry for $$y = 2x^2$ - 4x + 3$$?

Accepted Answer

$$x = 1$$

Question 13

Which of the following is the correct factorization of $$x^2 - 4x - 9$?

Accepted Answer

$$(x - (2 + \sqrt{13}))(x - (2 - \sqrt{13}))$$

Question 14

A parabola opens upward and has vertex $$(2, -5). $$Which equation could represent this parabola?

Accepted Answer

$$y = a(x-2)^2$ - 5$$ where $$a \u003e 0$$

Question 15

Given $$y = 2x^2$ + 8x + 7$$, what is the minimum value of the function?

Accepted Answer

$$-1$$

Question 16

Which of the following is NOT a possible $$x-$$intercept for $$y = x^2$ + 4$$?

Accepted Answer

$$x = 2$$

Question 17

If $$y = -x^2$ + 6x - 8$$, what is the maximum value and at what $$x$$ does it occur?

Accepted Answer

Maximum value $$1 at$$ $$x = 3$$

Question 18

Which of the following describes the transformation from $$y = x^2$ to y$$ = $$2(x-1)^2 + 1$?

Accepted Answer

Vertical stretch by $$2$$, right $$1$$, up $$1$$

Question 19

Using synthetic division, what is the quotient when $$x^3$$ - $$2x^2 - x + 2$ is divided by x - 1$?

Accepted Answer

$$x^2 - x - 2$

Quadratic Functions, Inequalities, and Zeros of Polynomial Functions – Precalculus Study Notes

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