i need the answer i am confused

Question

write the equation of the parabola in intercept form.

x-intercepts 12 and -6 and passes through (14,4)

Answer 1

y = a(x-12)(x+6)

to solve for a, plug in the point (14,4)

4 = a(14-12)(14+6) = a(2)(20) = 40a

a = 4/40 = 1/10

y = (1/10)(x-12)(x+6) is in y=a(x-h)(x-k) form where x=h and x= k are the x intercepts

for the y intercept

you need the constant term

y= (1/10)(x-12)(x+6)

multiply it all out

y = (1/10)(x^2 -6x -72)

= x^2/10 -6x/10 - 72/10

y = (1/10)x^2 - (3/5)x - 7.2

the y intercept = 7.2 or 72/10 = 36/5

that's

the form

y = ax^2 +bx + c where c= the y intercept

Answer 2

Equation of the parabola in intercept form: y = a(x - r)(x - s)

x-Intercepts: x = r = 12 and x = s = -6

y = a(x - r)(x - s) ==> y = a(x - r)(x - s) ==> y = a(x - 12)(x - (-6)) ==> y = a(x - 12)(x + 6)

Passes through: (x, y) = (14, 4)

y = a(x - 12)(x + 6) ==> 4 = a (14 - 12)(14 + 6) ==> 4 = a (2)(20) ==> a = 1/10

Equation of this parabola in intercept form: y = (1/10)(x - 12)(x + 6)