Write an equation of the parabola that passes through the point (1.5) and has x-intercepts 2 and 6. An equation of the parabola is $y=$

Answer 1

f(x) = ax² + bx + c. or. f(x) = a (x - h)²+ k where (h,k) is the vertex.

In this case it is easiest to use the two intercepts.

So f(x) = a (x - 2) (x - 6) we know also that the parabola passes through (1,5). So when x = 1, y = 5.

Putting those values in lets us find a.

5 = a (1-2) (1-6)

5 = a (-1) (-5)

So 5 = 5a

a = 1

Substituting a into the equation gives y = 1(x - 2) (x - 6) or. y = x² - 8x + 12

You may check this by graphing, or by substituting x = 2 and x = 6. Do you get 0 for y? and when x = 1, do you get 5 for y?

Answer 2

f(x) = a(x - 2)(x - 6)

5 = a(1 - 2)(5 - 6)

Can you solve for a and answer?