What is the minimum point of the graph of the equation y = 2x^2 + 8x + 9?

Question

(1) (2,33)
(2) (-2, 5)
(3) (2, 17)
(4) (-2, 1)

thanks alot

Answer 1

The minimum point occurs at x = -b/(2a)
a = 2 and b = 8
x = -8/(2*2)
x = -8/4
x = -2
That eliminates choices (1) and (3).
Replace x with -2 to find the y value.
y = 2(-2)^2 + 8(-2) + 9
y = 2(4) - 16 + 9
y = 8 - 16 + 9
y = 1
Answer: (-2,1)

Answer 2

You can always find the maximums and minimums of an equation by taking its derivative and setting to zero. This makes sense because the derivative is an equation for the slope, and where the slope is zero, the curve is a flat line. See?

For this equation, the derivative is y = 4x +8. Solve that for zero and you get -2. If you plug the -2 into the original equation, you get a y of 1. So that's your answer: (-2, 1), or answer (4).

Hope that helps!

Answer 3

take the derivative of the problem. Set it equal to zero to solve for critical points. Plug back into original problem. do a +/- test to find min, or you can just plug it in to a graphing calculater and find Min