Mathematics

Question

o find 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?

1 Answer

  • 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

    [tex]-4x^{2}+8x-25[/tex]

    This is a vertical parabola open downward

    The vertex is a maximum

    Find the vertex

    step 1

    Factor the leading coefficient -4

    [tex]-4(x^{2}-2x)-25[/tex]

    step 2

    Complete the square

    [tex]-4(x^{2}-2x+1-1)-25[/tex]

    step 3

    [tex]-4(x^{2}-2x+1)-25+4[/tex]

    [tex]-4(x^{2}-2x+1)-21[/tex]

    step 4

    Rewrite as perfect squares

    [tex]-4(x-1)^{2}-21[/tex]

    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