Question

Find the x-intercepts of the parabola with vertex (-7,45) and y-intercept (0,-200). Write your answer in this form: (x1, y1),(x2, y2). If necessary, round to the nearest hundredth.

Answer 1

Explanation:

bit lengthy but....

we know vertex is equal (h,k)

h=x . k=y

the vertex formula is f(x)= a(x-h)^2+k

lets plug in vertex... a(x+7)^2+45

we need to solve for (a) in order to make sure this will pass thru the coordinate (0,-200) and then from there we can get our x int.

the way we solve for a is to set the equation equal to the y int (-200)

f(x)=a(x+7)^2+45=-200

lets set x=0 because we already set y=-200

a(0+7)^2+45=-200

a(7)^2+45=-200

49a+45=-200

49a=-245

a=-5

Now lets rewrite the vertex form formula with a leading coefficient of -5

-5(x+7)^2+45

now graph this formula verify that it does indeed intersect (0.-200)

then check the table for your zeros or x int you will see that they are

(-10,0) and (-4,0)

or x+10=0 and x+4=0