Question

To find the minimum value of the quadratic expression −4x2+8x−25, Marla used the following steps to complete the square: Step 1: −4(x2+8x)−25 Step 2: −4(x2+8x+16−16)−25 Step 3: −4(x2+8x+16)+64−25 Step 4: −4(x+4)2+39 Did Marla use the correct steps to complete the square?

Answer 1

Answer:

Given:

x

2

+8x+15=0

x

2

+8x=−15

x

2

+8x+16=−15+16

x

2

+2×4x+4

2

=1

(x+4)

2

=1

x+4=±1

Hence, x=−4+1=−3 or x=−4−1=−5