Vertex forms 11th grade

Question

find the x-intervept of the probla form vertex (4,-1) and y - intercept (0,15). write your answer in this form (x1,y1) , (x2,y2). if necessary round to the nearest hundred

Answer 1

You need y = a(x - h)² + k the vertex form of the parabola, with vertex at point (h, k).

If the vertex is (4,-1) the equation becomes y = a(x - 4)² - 1

So now we need to find a, by using the given y intercept (0,15), so we substitute the point values to get

15 = a(0 - 4)² - 1

=> 15 = 16a - 1

=> 16 = 16a

=> a = 1

Hence our equation is y = (x - 4)² - 1

The x intercepts are when y = 0 so let's solve

0 = (x - 4)² -1

=> (x - 4)² = 1

=> (x - 4) = √1 = +1 or -1

=> x = +1 +4 or -1 + 4 = 5 or 3

Hence our x intercepts are (3,0) and (5,0).

I recommend Desmos graphing calculator as a great tool to experiment and/or check your work.