SOLUTION: Consider the parabola given by the equation: f(x)=-2x^2-10x-12 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point:

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider the parabola given by the equation: f(x)=-2x^2-10x-12 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point:       Log On


   

Question 1170151: Consider the parabola given by the equation: f(x)=-2x^2-10x-12
Find the following for this parabola:
A) The vertex:

B) The vertical intercept is the point:

C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas:

It is OK to round your value(s) to to two decimal places.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-2x%5E2-10x-12
Find the following for this parabola:
A) The vertex:
write it in vertex form by completing square
f%28x%29=-2%28x%5E2%2B5x%29-12
f%28x%29=-2%28x%5E2%2B5x%2Bb%5E2%29+-%28-2b%5E2%29-12.......b=5%2F2
f%28x%29=-2%28x%5E2%2B5x%2B%285%2F2%29%5E2%29+%2B2%285%2F2%29%5E2-12
f%28x%29=-2%28x%2B5%2F2%29%5E2+%2B2%2825%2F4%29-12
f%28x%29=-2%28x%2B5%2F2%29%5E2+%2B1%2F2 -> h=-5%2F2 and k=1%2F2
=> The vertex: at (-5%2F2 ,1%2F2)
B) The vertical intercept is the point:
will be at (0 ,y)
f%28x%29=-2x%5E2-10x-12
f%28x%29=-2%2A0%5E2-10%2A0-12
f%28x%29=-12+

C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas:
will be at (x ,0)
0=-2x%5E2-10x-12...factor
0=-2%28x%5E2%2B5x%2B6%29
0=-2%28x%5E2%2B3x%2B2x%2B6%29
0=-2%28%28x%5E2%2B3x%29%2B%282x%2B6%29%29
0=-2+%28x+%2B+3%29+%28x+%2B+2%29
=> x=-3 and x=-2
solutions: -3 ,-2