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)−2
Mathematics
johnnicerecolaso
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?
−
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

1. User Answers calculista
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
Stepbystep explanation:
we have
[tex]4x^{2}+8x25[/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+11)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(x1)^{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