What is the equation of the parabola in intercept form?

Question

X-intercept of 12 and -6; passes through (14,4)

Answer 1

The intercept form of a parabola is:

f(x) = a(x-r)(x-s)

where r and s are the intercepts. In this case, r =12 and s = -6

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

f(14) = a(14-12)(14+6) = a(2)(20) = 16a = 4 --> a = 4/40 = 0.1

therefore, f(x) = 0.1(x-12)(x+6)

Answer 2

since the zeros are at 12 and -6 we can write the equation in factored form y= a( x-12)(x+6)

We have the point (4,14) which we can use to solve for a

14= a( 4-12)(4+6)

14=a(-8)(10)

14 =-80a a= -14/80 =-7/40 or -.175 take your pick of which you want to use. I will use in fraction form

so equation is y =(-7/40)[ (x-12)(x+6) ]

If you plot this equation in desmos you will see that is satisfies your criteria