identify the vertex of the parabola defined by y=2x^(2)+8x+9

Question

a. (4,41)

b. (2, 33)

c. (-4,9)

d. (-2, 1)

Answer 1

To find the x-coordinate of the vertex, you use the formula -b/2a. (Remember that the standard form of a quadratic is y = ax² + bx + c.) So in this case b = 8 and a = 2.

-b/2a = -8/(2·2) = -8/4 = -2

Now to find the y-coordinate, simply plug the x-value into the quadratic equation.

y = 2x² + 8x + 9

y = 2(-2)² + 8(-2) + 9

y = 8 - 16 + 9

y = 1

So the vertex is at the point (-2, 1)     choice D

Answer 2

Hello, thank you for taking the time to post your question!

You can find the vertex using

x = -b/2a

x = -8 / 2(2) = -8/4 = -2

then plugging that back into the function yields

y = 2(-2)^2 + 8(-2) + 9

y = 2(4) – 16 + 9

y = 8 – 16 + 9

y = 17 – 16 = 1, meaning that the point we’re after here for the vertex is (-2,1)

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)