find the x-intercepts of the parabola with vertex (1,1) and y- intercept (0,-3). Write your answer in this form:(x1,y1)(x2,y2)

Question

when given a vertex and y intercept of parabola, use this form of the equation to find the x- intercepts

 

(y-k)=a(x-h)^2

 

where a=0

Answer 1

The vertex of a parabola has coordinates (h, k).  You can obtain the values of h and k, using the vertex formula you have here.

 

y = a(x - h)² + k

 

a = 0

h = 1

k = 1

 

 

Plugging in these values into the vertex form, we get

 

y = 0(x - 1)² + 1

 

 

Because any value multiplied by zero is always zero, we get

 

y = 1

 

 

This is a horizontal line.  Since horizontal lines never crosses or touches the x-axis, there will be no x-intercepts.

 

 

Note: 

In order for a parabola to have any x-intercepts,  a≠0.