SOLUTION: How do I enter this problem to work it? Use formula x=-b/2a to find the coordinates of the vertex for the parabola defined by the quadratic function f(x)=2x^2+4x-15. Substitute

Algebra ->  Rational-functions -> SOLUTION: How do I enter this problem to work it? Use formula x=-b/2a to find the coordinates of the vertex for the parabola defined by the quadratic function f(x)=2x^2+4x-15. Substitute       Log On


   

Question 88766: How do I enter this problem to work it?
Use formula x=-b/2a to find the coordinates of the vertex for the parabola defined by the quadratic function f(x)=2x^2+4x-15. Substitute this value into the f(x) to find the y coordinate of the vertex. Plot two points to the left and right of the vertex. Do the graph of the parabola. HELP!!!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex of the parabola defined by:
f%28x%29+=+2x%5E2%2B4x-15 Compare this with the general form:
f%28x%29+=+ax%5E2%2Bbx%2Bc...and you can see that: a = 2, b = 4, and c = -15
Now substitute a and b into the formula for the x-coordinate of the vertex:-b%2F2a
x+=+-4%2F2%282%29
x+=+-4%2F4
x+=+-1 This is the x-coordinate of the vertex. Substitute this value of x into the given quadratic equation and solve for f(x), this is the same as the y-coordinate.
f%28-1%29+=+2%28-1%29%5E2%2B4%28-1%29-15 Evaluate.
f%28-1%29+=+2-4-15
f%28-1%29+=+-17
The coordinates of the vertex are:
(-1, -17)...and the equation of the line of symmetry is:x+=+-1
The graph looks like this:
graph%28400%2C400%2C-5%2C5%2C-20%2C5%2C2x%5E2%2B4x-15%29
To plot two points to the left and to the right of the vertex (line of symmetry), choose four values of x-coordinate, such as:
x = 0
x = -2
x = 1
x = -3
and for each one of these, find the corresponding y-coordinate (f(x)) and these will give you the coordinates of the four points.
I'll do one and you can finish the rest.
Substitute x = -3
f%28-3%29+=+2%28-3%29%5E2%2B4%28-3%29-15 Evaluate.
f%28x%29+=+2%289%29%2B%28-12%29-15
f%28x%29+=+18-12-15
f%28x%29+=+-9
The coordinates of this point are: (-3, -9)