Determine equation of quadratic function

the parabola intersects the x-axis at (1,0) and (3,0) and passes through point (4,-6).

Hi,

y = a(x - 1)(x - 3)

-6 = a(4 - 1)(4 - 3)

-6 = 3a

a = -2

y = -2((x - 1)(x - 3) <==ANSWER in intercept form

y = -2x² + 8x - 6 <==ANSWER

I hope that helps!! :-)

Since the parabola intersects the x-axis at (1, 0) and (3, 0), x = 1 and x = 3 are roots to the parabola, and, furthermore, x - 1 and x - 3 are factors of said parabola by the Factor Theorem.

So, we can write:
f(x) = a(x - 1)(x - 3), for some constant a.

To determine a, use the fact that (4, -6) being on the parabola implies that f(x) = -6 when x = 4. This gives:
-6 = a(4 - 1)(4 - 3) ==> a = -2.

Therefore:
f(x) = -2(x - 1)(x - 3).

I hope this helps!

y==a(x-1)(x-3)
-6=a(4-1)(4-3)
-6=3a
a=-2

y=-2(x-1)(x-3)
y=2x^2-8x+6

y = a(x - 1)(x - 3)
-6 = a(4 - 1)(4 - 3)
-6 = a*3*1
a = -2

so
y = -2(x - 1)(x - 3)