Question

O find the minimum value of the quadratic expression −4x2+8x−25,

Answer 1

Answer:

Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x

Step-by-step explanation:

we have

$-4x^{2}+8x-25$

This is a vertical parabola open downward

The vertex is a maximum

Find the vertex

step 1

Factor the leading coefficient -4

$-4(x^{2}-2x)-25$

step 2

Complete the square

$-4(x^{2}-2x+1-1)-25$

step 3

$-4(x^{2}-2x+1)-25+4$

$-4(x^{2}-2x+1)-21$

step 4

Rewrite as perfect squares

$-4(x-1)^{2}-21$

the vertex is the point (1,-21)

so

The maximum value of the quadratic equation is (1,-21)

therefore

Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x