Question

Consider the graph of the following quadratic equation y=-xpower of 2 - 10x + 24 What is the y-value of the vertex

Answer 1

The y-value of the vertex is 49

Explanation:

The given quadratic function is

`y=-x^2-10x+24`

We complete the square to find the vertex.

First factor
`-1` from the first two terms.

`y=-(x^2+10x)+24`

Add and subtract the square of half the coefficient of x.

`y=-(x^2+10x+5^2-5^2)+24`

`y=-(x^2+10x+5^2)--5^2+24`

Recognize the perfect square trinomial.

`y=-(x+5)^2+25+24`

`y=-(x+5)^2+49`

The function is now of the form;

`y=a(x-h)^2+k`, where (h,k)=(-5,49) is the vertex.

The y-value of the vertex is 49