Quadratic Functions: identify vertex, x-intercept(s) of....

[juliaann1987]

Identify the vertex and x-intercept(s).

f(x) = (1/4)x^2 - 2x - 12

When I work this problem down I am getting the correct value for the x in the vertex but I'm getting something wrong in the y of the vertex. Any suggestions????

 

[stapel]

Re: Quadratic Functions: identify vertex, x-intercept(s) of.

When I work this problem down I am getting the correct value for the x in the vertex but I'm getting something wrong in the y of the vertex. Any suggestions?

Please reply showing your steps and final answers, so the tutors can provide suggestions on how to correct whatever the error(s) might be.

Thank you.

Eliz.

 

[juliaann1987]

f(x) = (1/4)x^2 - 2x - 12
(1/4)
x^2 - 8x -48
(x^2 - 8x + 16 - 16) -48
(x^2 - 8x +16) - 16 - 48
(x - 4)^2 - 64




(That is divided by (1/4) at the top)

 

[Mrspi]

Re: Quadratic Functions: identify vertex, x-intercept(s) of.

Identify the vertex and x-intercept(s).

f(x) = (1/4)x^2 - 2x - 12

When I work this problem down I am getting the correct value for the x in the vertex but I'm getting something wrong in the y of the vertex. Any suggestions????

I tend to do this kind of problem "step-by-step."

So, let's substitute y for f(x):
y = (1/4)x² - 2x - 12

Next, let's get the coefficient of x² to be 1. Multiply both sides of the equation by 4:
4y = 4(1/4)x² - 4(2x) - 4(12)
4y = x² - 8x - 48

Then, get the terms containing x on one side of the equation, and everything else on the other side. Add 48 to both sides of the equation:
4y + 48 = x² - 8x

Complete the square on the right side of the equation. Divide the coefficent of x by 2, SQUARE it, and add the result to both sides of the equation. Half of -8 is -4, and (-4)² is 16. Add 16 to both sides of the equation:
4y + 48 + 16 = x² - 8x + 16

Simplify the left side, and write the right side as the square of a binomial:
4y + 64 = (x - 4)²

Subtract 64 from both sides:
4y = (x - 4)² - 64

Multiply both sides of the equation by 4 (or, multiply by 1/4):

y = (1/4) (x - 4)² - 16

That gives you the equation of the parabola in VERTEX form...the vertex is at (-4, -16)....is that what you got?

 

[juliaann1987]

the vertex is supposed to be (4, -16)

 

[stapel]

I would guess that this is a typo in Mrs. Pi's solution.

Fortunately, since she has provided you with a complete worked solution, you can follow through the logic and review the final vertex-form of the equation. Then read off the values of h and k for the vertex.

Eliz.