Ofind the minimum value of the quadratic expression −4x2+8x−25,
−
4
x
2
+
8
x
−
25
,
marla used the following steps to complete the square:

step 1: −4(x2+8x)−25
−
4
(
x
2
+
8
x
)
−
25

step 2: −4(x2+8x+16−16)−25
−
4
(
x
2
+
8
x
+
16
−
16
)
−
25

step 3: −4(x2+8x+16)+64−25
−
4
(
x
2
+
8
x
+
16
)
+
64
−
25

step 4: −4(x+4)2+39
−
4
(
x
+
4
)
2
+
39

did marla use the correct steps to complete the square?

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

This is a vertical parabola open downward

The vertex is a maximum

Find the vertex

step 1

Factor the leading coefficient -4

step 2

Complete the square

step 3

step 4

Rewrite as perfect squares

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

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17