25 POINTS~!!! Graph h(x)=−x^2+8. Use the parabola tool then choose the vertex followed by one point on the parabola.

The point of the vertex is (3, -1).

Parabola

Parabola is the locus of a point that moves so that it is always the same distance from a fixed point and fixed-line. The fixed point is called the focus and the fixed line is called the directrix. And the equation will be quadratic.

Quadratic equation

Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation. The general form of the quadratic equation is ax² + bx + c.

Given

h(x)=(x−2)(x−4) is equation of parabola.

To find

The point of the vertex.

How to find the point of the vertex?

h(x)=(x−2)(x−4)

simplify the equation

h(x) = x² - 6x + 8

Then add and subtract 9.

h(x) = x² - 6x + 9 - 9 + 8

h(x) = (x -3)² -1

Then the point of the vertex is (3, -1).

Step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1