Question

1. use the zeros for the function graphed below to write the equation in standard form y = ax² + bx + c

Explanation:

Step1: Identify zeros from graph

Zeros at $x=0$ and $x=20$

Step2: Write factored form

$y = ax(x - 20)$

Step3: Find vertex coordinates

Vertex at $(10, -10)$ (midpoint of zeros, y-value from graph)

Step4: Solve for a

Substitute $(10, -10)$: $-10 = a(10)(10 - 20) \Rightarrow -10 = -100a \Rightarrow a = \frac{1}{10}$

Step5: Expand to standard form

$y = \frac{1}{10}x(x - 20) = \frac{1}{10}x^2 - 2x$

Answer:

$y = \frac{1}{10}x^2 - 2x$