Question

use (-x^2 + 2x + 5) to answer the following questions.
(x = -\frac{b}{2a})
use your value of (x) in the equation to find the (y)-coordinate of the vertex.
(f(x) = a(x - h)^2 + k)

1. what are the coordinates of the vertex?

enter your answer as an ordered pair.

Explanation:

Step1: Identify a, b values

For $f(x)=-x^2+2x+5$, $a=-1$, $b=2$

Step2: Calculate x-coordinate

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

Step3: Calculate y-coordinate

Substitute $x=1$ into $f(x)$
$f(1)=-(1)^2+2(1)+5 = -1+2+5=6$

Answer:

$(1, 6)$