Question

Find the x-intercept of the parabola with vertex (1,-17) and y-intercept (0,-16). type your answer in this form: (x1,y1), (x2,y2). If necessary, round to the nearest hundredth.

Answer 1

Format for the equation of a parabola is : y = a(x - h)² + k where (h, k) is the vertex. 

First, we plug in the value of the vertex, (1, -17) into the equation:
y = a(x - 1)² - 17

Next, we need to look for the value of a:
To find "a", we need to find a point on the graph. In this case, the graph has a y-intercept of (0,-16), we will use this point.
-16 = a (0 - 1)² - 17
-16 = a - 17
a = -16 + 17
a = 1

Now, we plug in the value of "a" into the equation and the equation is complete:
y = (x - 1)² - 17

To find the x-intercept of the equation, we will plug in 0 for the value of y:
0 = ( x- 1)² - 17
(x - 1)² = 17
x- 1 = ±√17
x = √7 - 1 or -√7 -1
x = 1.65 or -3.65 (nearest hundredth)

Answer: The x-intercept are (1.65, 0) and (-3.65, 0)