A parabola that has x− intercepts (5,0) and (−6,0) and y− intercept (0,−1).
The equation of parabola is [tex]y=\frac{1}{30}(x-5)(x+6)[/tex]
parabola x intercept form is:
[tex]y=a(x-x_{1} )(x-x_{2} )[/tex]
[tex]x_{1}[/tex] and [tex]x_{2}[/tex] being the x intercepts
x intercepts are (5,0) and (−6,0)
[tex]y=a(x-5)(x-(-6))\\y=a(x-5)(x+6)[/tex]
To solve for a substitute with the other coordinate they give you (0, -1)
[tex]-1=a(0-5)(0+6)\\-1=-30a\\a=\frac{1}{30}[/tex]
So, [tex]y=\frac{1}{30}(x-5)(x+6)[/tex]
Therefore, the equation of parabola is [tex]y=\frac{1}{30}(x-5)(x+6)[/tex]
For more information:
https://brainly.com/question/14481138
