Find the x-intercept of the parabola with vertex (3,-2) and y-intercept (0,7)

The x-intercepts (there are 2 of them) are located at (3±√2, 0)

Step-by-step explanation:

In order to find the x-intercepts, we have to factor the equation to solve it for x.  However, at the present time, we have no equation to factor; we only have the vertex (h, k) and a coordinate (0, 7).  So we will use those to find the equation of the parabola.  If you graph the points, it's apparent that this is a positive x-squared parabola of the vertex form:

We need to solve for a to get the correct equation.  Filling in our info gives us:

so

7 = a(9) - 2 and

9 = 9a so

a = 1.  The equation for our parabola is

The easiest way to find the x-intercepts (factor it) is to write it in standard form which is

In order to do that we have to expand that binomial by FOILing and we get

which simplifies to

In order to factor that you have to throw it into the quadratic formula.  That looks like this:

which simplifies to

The square root of 8 simplifies:

and dividing everything but the radicand (the number under the square root) by 2 gives you both of your x-intercepts:

x = 3 ± √2

the graph on the bottom right

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.