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

Beginner2022-06-20Added 22 answers

From the roots ($x$ intercepts), you can write the equation of the parabola as: $y=a(x+1)(x-5)$

When $x=0$ (this is the $y$ intercept), $a(-5)=5$, so $a=-1$.

So $y=-(x+1)(x-5)$

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 $\frac{-1+5}{2}=2$).

When $x=0$ (this is the $y$ intercept), $a(-5)=5$, so $a=-1$.

So $y=-(x+1)(x-5)$

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

Beginner2022-06-21Added 11 answers

Since$x=-1$ and $x=5$ are zeros of your parabola, your parabola is

$y=a(x+1)(x-5)$

Since your $y$-intercept is $(0,5)$ you get

$5=a(1)(-5)$

which implies

$a=-1$

Thus your equation is

$y=-(x+1)(x-5)$

You may write it in standard form

$y=-{x}^{2}+4x+5$

$y=a(x+1)(x-5)$

Since your $y$-intercept is $(0,5)$ you get

$5=a(1)(-5)$

which implies

$a=-1$

Thus your equation is

$y=-(x+1)(x-5)$

You may write it in standard form

$y=-{x}^{2}+4x+5$