Answer:
Explanation:
Equation
y = x^2 + 8x + 7 Put brackets around the first two terms
y = (x^2 + 8x) + 7 Take 1/2 the linear term's coefficient (8)
8/2 = 4 Put this result inside the brackets and square
y = (x^2 + 8x + 4^2) + 7 Take - 4^2 and add it to the seven.
y = (x^2 + 8x + 16) + 7 - 16 What you did, did not change the eqiuation
Y = (x^2 + 8x + 16) - 9 The first 3 terms make a perfect square
y = (x + 4)^2 - 9
The minimum should be at - 4,-9 Just to make sure it is, I'll graph the original equation. The y intercept should be at 7 and the two x roots should x = + 3 - 4 and x = -3 - 4. or x = -1 and x = - 7
Let's see if this all checks out.
Graph of original equation.