 Misael Matthews

2022-06-19

How to find the y of the vertex. How can I find the y? The x intercepts are (-1,0) (5,0) and the y intercept is (0,5) and the x of the vertex is 2. Jaylee Dodson

From the roots ($x$ intercepts), you can write the equation of the parabola as: $y=a\left(x+1\right)\left(x-5\right)$
When $x=0$ (this is the $y$ intercept), $a\left(-5\right)=5$, so $a=-1$.
So $y=-\left(x+1\right)\left(x-5\right)$
Set $x=2$ for the vertex (turning point) to find $y=9$.
(From what you wrote, I assume you know how to find the $x$ coordinate of the vertex or turning point, but just for completeness, it is the arithmetic mean (average) of the two real roots, so here it is simply $\frac{-1+5}{2}=2$). Zion Wheeler

Since$x=-1$ and $x=5$ are zeros of your parabola, your parabola is
$y=a\left(x+1\right)\left(x-5\right)$
Since your $y$-intercept is $\left(0,5\right)$ you get
$5=a\left(1\right)\left(-5\right)$
which implies
$a=-1$
$y=-\left(x+1\right)\left(x-5\right)$
You may write it in standard form
$y=-{x}^{2}+4x+5$

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