Quadratic functions

Question

In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 2x² + 20x + 5

Answer 1

For this, I use the formula x = -b ÷ 2a, in this case you can substitute 20 for b and 2 for a.

So then you get:

x = -20 ÷ 2(2), which gives you -5.

From there, you can substitute -5 for x.

f(-5) = 2(-5)² + 20(-5) + 5, which is 2(25) - 100 + 5, which is 50 - 100 + 5, which is -50 + 5, which is -45.

So f(-5) = -45. Your vertex is now (-5, -45).

Hope this helps!

Answer 2

complete the square, factor out 2, then add and subtract half 10 squared:

f(x) = 2x^2 +20x +5

= 2(x^2 +10x + 25) + 5 -2(25)

= 2(x+5)^2 -45

in vertex form, =a(x-h)^2 + k

with vertex = (h,k) = (-5,-45)

Answer 3

Uses Completion of the Square to transform to vertex form.