Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.
Answers:
The range is {y| y ≥ –1}.
The function decreases over the interval (–∞, 3).
The vertex is (3, –1).

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.
Which statements about the function are true? Select three options.
Answers:
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.

The steps in writing f(x)=18x+3x2 in vertex form are shown, but a value is missing in the last step.
Write the function in standard form.
Factor a out of the first two terms. f(x)=3(x2+6x)
Form a perfect square trinomial. (six-halves) squared
f(x)=3(x2+6x+9)−3(9)
Write the trinomial as a binomial squared. f(x)=3(x+___)2−27
What is the missing value in the last step?
Answer: 3

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?
Answer: {–2, 10}

Which is the graph of the function f(x) = x2 + 2x + 3?
Answer: 1st graph

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
Answer: {–7, 1}

What are the solutions to the quadratic equation 4(x + 2)2 = 36
Answer: x = −5 and x = 1

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?
Answer: The discriminant is 73, so the equation has 2 real solutions.

What is the y-value of the vertex of the function f(x)=−(x−3)(x+11)?
Answer: 49

What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?
Answer: (4, 0) and (−9, 0)