Question 37646: Please help me with this one.
Find the equation of the axis of symmetry, the coordinates of the vertex, and the coordinates of the x-intercepts, if they exist, for each parabola.
1. f(x)=2x^-3x-14
Thanks very much in advance
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the equation of the axis of symmetry, the coordinates of the vertex, and the coordinates of the x-intercepts, if they exist, for each parabola.
1. f(x)=2x^2-3x-14
Rewrite as y+14 = 2(x^2-(3/2)x
Complete the squareon the right side and maintain the equality, as follows:
y+14+2(3/4)^2 = 2(x^2-(3/2)x+(3/4)^2)
Simplify as follows:
y+14+9/8=2[x-(3/4)]^2
y+121/8 = 2[x-(3/4)]^2
Axis of symmetry is x=3/4
Vertex is (3/4,-121/8)
X-intercepts?
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=121 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 3.5, -2.
Here's your graph:
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Hope this helps.
Cheers,
Stan H.
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