SOLUTION: transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.      Log On


   

Question 936233: transform the quadratic function y=-2x^2-12x-10 into vertex form. find the vertex, x and y intercepts.
Found 3 solutions by ewatrrr, srinivas.g, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Previously Posted
y= -2x^2-12x-10 P(0, -10) y-intercept
y = -2(x+3)^2 + 18 - 10
y = -2(x+3)^2 + 8
V(-3,8)
......
0 = -2(x+3)^2 + 8
4 =(x+3)^2
± 2 = x+3
-3 ± 2 = x
P(-5,0) and P(-1,0) x-intercepts

Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
step 1 : determination of vertex
+y=+-2x%5E2-12x-10
+y=+-2%28x%5E2%2B6x%2B5%29
+y=+-2%28x%5E2%2B2%2Ax%2A3%2B3%5E2-4%29
+y=+-2%28%28x%2B3%29%5E2-4%29
+y=+-2%28x%2B3%29%5E2-2%28-4%29
+y=+-2%28x%2B3%29%5E2%2B8+
vertex form ++y=a%28x-h%29%5E2%2Bk
vertex =(h,k)
hence vertex (h,k) =(-3,8)
step 2
determination of y-intercept:
keep x=o in the y= -2x^2-12x-10
y= -2*0-12*0 -10
y= -10
hence y-intercept = -10
step 3
Determination of x-intercept:
keep y= 0 in y= -2x^2-12x-10
+0=+-2x%5E2-12x-10
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B-12x%2B-10+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-12%29%5E2-4%2A-2%2A-10=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+64+%29%29%2F2%5C-2+=+-5
x%5B2%5D+=+%28-%28-12%29-sqrt%28+64+%29%29%2F2%5C-2+=+-1

Quadratic expression -2x%5E2%2B-12x%2B-10 can be factored:
-2x%5E2%2B-12x%2B-10+=+-2%28x--5%29%2A%28x--1%29
Again, the answer is: -5, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-12%2Ax%2B-10+%29


hence x-intercepts are -5, -1

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the vertex form:
y=a%28x-h%29%5E2%2Bk
y=-2x%5E2-12x-10
y=-2%28x%5E2%2B6x%29-10
y=-2%28x%5E2%2B6x%2B_%29-_-10
y=-2%28x%5E2%2B6x%2B9%29-2%2A%28-9%29-10
y=-2%28x%2B3%29%5E2%2B18-10
y=-2%28x%2B3%29%5E2%2B8
vertex is at (-3,-19)

y-intercept is 8
x-intercept is:
0=-2x%5E2-12x-10
2x%5E2%2B12x%2B10=0
2x%5E2%2B2x%2B10x%2B10=0
%282x%5E2%2B2x%29%2B%2810x%2B10%29=0
2x%28x%2B1%29%2B10%28x%2B1%29=0
%282x%2B10%29%28x%2B1%29=0
2%28x%2B5%29%28x%2B1%29=0
solutions:
if %28x%2B5%29=0=> x=-5
if %28x%2B1%29=0=> x=-1
so, x-intercepts are: x=-5 and x=-1

+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+10%2C+-2x%5E2-12x-10%29+