Write the formula for the parabola that has x- intercepts (1.3,0) and (−1.3,0), and y- intercept (0,169)

Question

So the equation starts like y=

Answer 1

Write the formula for the parabola that has x- intercepts (1.3,0) and (−1.3,0), and y- intercept (0,169)

 

Solution:

 

let me start by the following correction:

 

The y intercept is (0,1.69) and not (0,169)

So the intercept form of the quadratic equation is y=a(x-p)(x-q)

 

where (-1.3,0)=(p,0) and (1.3,0) is (q,0); then p=-1.3, and q=1.3

 

With the vertex being at the y axis and the intercepts at the x axis means that the parabola opens down. then 1.69=a(0+1.3)(0-1.3), 1.69=-1.69 a, a=-1

 

 

Substituting, y=-1(x+1.3)(x-1.3) note that this is difference of two squares y=-[x²-(1.3)²] , y=-(x²-1.69), y=-x²+1.69

Answer 2

The vertex, as well as the y-intercept, is at (0, 169)   Note: 0 is half way between -1.3 and 1.3.

y = a(x - 0)² + 169

0 = a(-1.3 - 0)² + 169

0 = a(1.69) + 169

-169 = 1.69a

-100 = a

 

y = -100x² + 169