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](/tpl/images/0438/9210/7010a.png)
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](/tpl/images/0438/9210/17c8b.png)
step 2
Complete the square
![-4(x^{2}-2x+1-1)-25](/tpl/images/0438/9210/b9561.png)
step 3
![-4(x^{2}-2x+1)-25+4](/tpl/images/0438/9210/78a08.png)
![-4(x^{2}-2x+1)-21](/tpl/images/0438/9210/cec20.png)
step 4
Rewrite as perfect squares
![-4(x-1)^{2}-21](/tpl/images/0438/9210/6c5da.png)
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