Question

unit 8 hw 2 - graphing quadratic functions
directions: show all work in order to receive full credit.

1. graph: $f(x) = -x^2 -2x + 3$

a. what are the zeros?

1. graph: $f(x) = x^2 + 4x + 3$

a. what is the vertex?

1. graph: $f(x) = 3x^2 + 5x - 2$

a. what is the axis of symmetry?

1. graph: $f(x) = -2x^2 + 4x + 8$

a. what is the parent function?

Explanation:

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Problem 1: $f(x) = -x^2 -2x +3$

Step1: Factor the quadratic

$-(x^2 +2x -3) = -(x+3)(x-1)$

Step2: Solve for zeros (set $f(x)=0$)

$-(x+3)(x-1)=0 \implies x+3=0 \text{ or } x-1=0$

Answer:

(Problem 1a):
$x=-3$ and $x=1$

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Problem 2: $f(x) = x^2 +4x +3$

Step1: Find x-coordinate of vertex

For $ax^2+bx+c$, $x=-\frac{b}{2a} = -\frac{4}{2(1)} = -2$

Step2: Find y-coordinate of vertex

$f(-2) = (-2)^2 +4(-2)+3 = 4-8+3 = -1$