Question

find the x intercepts of the parabola with vertex (5,-12) and y-intercept (0,63) write your answer in this form: (x1,y1),(x2,y2) if necessary, round to the nearest hundredth

Answer 1

Let’s find the x-intercepts of the parabola with vertex (5,-12) and y-intercept (0,63).

The vertex form of a parabola is given by the equation y = a(x-h)^2 + k, where (h,k) is the vertex. Substituting the given vertex (5,-12) into this equation, we get y = a(x-5)^2 - 12.

To find the value of ‘a’, we can use the given y-intercept (0,63). Substituting x=0 and y=63 into the equation above, we get 63 = a(0-5)^2 - 12. Solving for ‘a’, we find that a = 3.

So, the equation of the parabola is y = 3(x-5)^2 - 12.

To find the x-intercepts, we set y=0 and solve for x. This gives us 0 = 3(x-5)^2 - 12. Solving this quadratic equation, we find that x = 5 + sqrt(4) or x = 5 - sqrt(4).

So, the x-intercepts of the parabola are approximately (6.41,0) and (3.59,0), rounded to the nearest hundredth.

Explanation: