Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

Question

mathmale · Answer

You'll probably have the find the equation of this parabola first.  Once you have that, you'll find the x-intercepts.  

Focus on finding the equation of the parabola now.

If the y-intercept is (0,-6), then regard that point as one point on the parabola.

Use the vertex form of the equation of a parabola:$$y=a(x-h)^2+k$$

mathmale · Answer

where a is a constant, h is the x-coordinate of the vertex and k is the y-coord. of the vertex.

pbonnette · Answer

So it would be -6=a(x-1)^2+(-9)? @mathmale

mathmale · Answer

Looks good, except that "x" has a known value.

You must somehow find the value of "a."  Think about how you might do that.  subst. the given value for x first, and then find a.

pbonnette · Answer

How do I do that?

mathmale · Answer

Made a mistake.
You have 2 points:  (0,-6) and (1,-9).  Have you inserted all four values 0, -6, 1, -9 into your equation?

mathmale · Answer

If you do this, you'll have only ONE unknown, and that unknown will be the coefficient "a."

Find this "a."

Then write out the equation of the parabola.  It must involve (x, y) as well as (1,-9).

Last, set y=0 and solve the resulting equation for x.  Those will be the x-coord. of your x-intercepts.

Have to get off the 'Net now.  Good luck!

pbonnette · Answer

One is the vertex and the other is the Y-intercepy