SOLUTION: Given the quadratic function f(x) = -2x2 - 12x - 10 a. Use “completing the squares” to convert the quadratic function into vertex form b. State the vertex c. Find the x- a

Algebra ->  Rational-functions -> SOLUTION: Given the quadratic function f(x) = -2x2 - 12x - 10 a. Use “completing the squares” to convert the quadratic function into vertex form b. State the vertex c. Find the x- a      Log On


   

Question 1064208: Given the quadratic function f(x) = -2x2 - 12x - 10
a. Use “completing the squares” to convert the quadratic function into vertex form
b. State the vertex
c. Find the x- and y-intercepts
d. Graph the function
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-2%28x%5E2%2B6x%2B5%29
The term to complete the square is 9. Do this inside the parentheses.
-2%28x%5E2%2B6x%2B5%29
-2%28x%5E2%2B6x%2B9-9%2B5%29
-2%28%28x%2B3%29%5E2-4%29
cross%28f%28x%29=-2%28x%2B3%29%5E2%2B2%29
f%28x%29=-2%28x%2B3%29%5E2%2B8
Vertex is (-3,2).
Vertex is (-3,8).

Find x intercepts using cross%28-2%28x%2B3%29%5E2%2B2=0%29,-2%28x%2B3%29%5E2%2B8=0;

Find any y intercepts by evaluating f%280%29.


EDITED GRAPH; FIXED ARITHMETIC MISTAKE
graph%28300%2C300%2C-6%2C6%2C-2%2C10%2C-2%28x%2B3%29%5E2%2B8%29

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
f%28x%29 = %28-2%29%2A%28x%5E2%2B6x%2B5%29 = %28-2%29%2A%28%28x%5E2+%2B+6x+%2B+9%29+-+9+%2B+5%29  = %28-2%29%2A%28%28x%2B3%29%5E2-4%29 = %28-2%29%2A%28x%2B3%29%5E2+%2B+8.

Vertex is  (-3,8).


Find x-intercepts using  -2%28x%2B3%29%5E2%2B8 = 0. They are x= -5 and x= -1.


Find y-intercepts by evaluating f%280%29 = -10.



graph%28300%2C300%2C+-6%2C+6%2C+-15%2C+15%2C%0D%0A+++++++++-2x%5E2+-+12x+-+10%0D%0A%29

Calculations by "josgarithmetic" are wrong.

Plot by "josgarithmetic" is wrong.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Given the quadratic function f(x) = -2x2 - 12x - 10
a. Use “completing the squares” to convert the quadratic function into vertex form
b. State the vertex
c. Find the x- and y-intercepts
d. Graph the function 
Correct answer: Equation is: y+=+-+2%28x+%2B+3%29%5E2+%2B+8, after completing the square, so: highlight_green%28matrix%281%2C3%2C+%22Vertex%22%2C+%22=%22%2C+%22%28-+3%2C+8%29%22%29%29

After using a method your choice, you should get: