SOLUTION: PROBLEM: A) WRITE THE FUNCTION IN THE FORM f(x)=a(x-h)^2+k BY COMPLETING THE SQUARE. B) THEN IDENTIFY THE VERTEX. p(x)= -5x^2-10x-13 PLEASE HELP!! I'M JUST REALLY NOT UNDERST

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: PROBLEM: A) WRITE THE FUNCTION IN THE FORM f(x)=a(x-h)^2+k BY COMPLETING THE SQUARE. B) THEN IDENTIFY THE VERTEX. p(x)= -5x^2-10x-13 PLEASE HELP!! I'M JUST REALLY NOT UNDERST      Log On

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Question 138931: PROBLEM:
A) WRITE THE FUNCTION IN THE FORM f(x)=a(x-h)^2+k BY COMPLETING THE SQUARE.
B) THEN IDENTIFY THE VERTEX. p(x)= -5x^2-10x-13
PLEASE HELP!! I'M JUST REALLY NOT UNDERSTANDING THIS WHOLE COMPLETE THE SQUARE THING, IT JUST ALL SEEMS SO FORIEGN?? THANKS
lj23kfuller@yahoo.com
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
p%28x%29=+-5x%5E2-10x-13

Step 1: Divide through by the lead coefficient

p%28x%29%2F%28-5%29=+x%5E2%2B2x%2B13%2F5


Step 2: Divide the coefficient on the 1st degree term by 2, then square the result. Add this result to both sides of the equation. %282%2F2%29%5E2=1%5E2=1

%28p%28x%29%2F%28-5%29%29%2B1=+x%5E2%2B2x%2B1%2B13%2F5

Step 3: Factor the perfect square trinomial:


%28p%28x%29%2F%28-5%29%29%2B1=+%28x%2B1%29%5E2%2B13%2F5

Step 4: Solve for p(x):

%28p%28x%29%2F%28-5%29%29=+%28x%2B1%29%5E2%2B13%2F5-1
%28p%28x%29%2F%28-5%29%29=+%28x%2B1%29%5E2%2B8%2F5
p%28x%29=+-5%28x%2B1%29%5E2-8

So a=-5 and k=-8, and the vertex is at (h, k), so (-1,-8) [-1 because the form is x - h, and we have x + 1 which is to say x - (-1).]