Question

name: camila boroaperiod: 7algebraunit 8 hw 2 - graphing quadratic functionsdirections: show all work in order to receive full credit.1. graph: $f(x) = -x^2 -2x + 3$a. what are the zeros?2. graph: $f(x) = x^2 + 4x + 3$a. what is the vertex?3. graph: $f(x) = 3x^2 + 5x - 2$a. what is the axis of symmetry?4. graph: $f(x) = -2x^2 + 4x + 8$a. what is the parent function?

Explanation:

1. Problem 1a: Find zeros of $f(x)=-x^2-2x+3$

Step1: Set $f(x)=0$

$-x^2 - 2x + 3 = 0$

Step2: Multiply by -1

$x^2 + 2x - 3 = 0$

Step3: Factor quadratic

$(x+3)(x-1)=0$

Step4: Solve for $x$

$x+3=0 \implies x=-3$; $x-1=0 \implies x=1$

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2. Problem 2a: Verify vertex of $f(x)=x^2+4x+3$

Step1: Use vertex $x$-formula

$x = -\frac{b}{2a} = -\frac{4}{2(1)} = -2$

Step2: Find $f(-2)$

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

Step3: Confirm vertex

Vertex is $(-2,-1)$

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3. Problem 3a: Find axis of symmetry for $f(x)=3x^2+5x-2$

Step1: Use axis formula

$x = -\frac{b}{2a} = -\frac{5}{2(3)}$

Step2: Simplify

$x = -\frac{5}{6}$

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4. Problem 4a: Identify parent function

Step1: Recognize quadratic base form

The parent function of all quadratic functions is the simplest quadratic.

Answer:

1. Problem 1a: $x=-3$ and $x=1$
2. Problem 2a: $(-2, -1)$ (verified as correct)
3. Problem 3a: $x=-\frac{5}{6}$
4. Problem 4a: $f(x)=x^2$