AHHH!! FACTORr?

Question

factor f(x)= f(x)= 2x^2 +4x+7

i need to find the vertex, steps, x/y interceptd n the max/min value

Answer 1

You can't factor this over the rationals because
b²-4ac = 16 - 56 < 0.
But let's answer the other parts.
f(x) = 2(x²+2x) + 7
Now complete the square inside the parentheses:
f(x) = 2(x²+2x+1) + 5
= 2(x+1)² + 5
So the vertex is at x = -1, y = 5.
Since a = 2, this is the minimum point on the curve.
There is no x intercept for f(x) since its
roots are complex, but the y intercept is
2(1) + 5 = 7.