Answer:
The zeros are the points where the parabola intercepts the x-axis.
[tex]\sf x = 7 \implies x - 7 = 0[/tex]
[tex]\sf x = 1 \implies x - 1 = 0[/tex]
[tex]\sf \implies y = a(x - 7)(x - 1)[/tex] where a is some constant
If the parabola passes through point (3, 4) then:
[tex]\sf \implies a(3 - 7)(3 - 1) = 4[/tex]
[tex]\sf \implies a(-4)(2) = 4[/tex]
[tex]\sf \implies -8a = 4[/tex]
[tex]\sf \implies a = -\dfrac12[/tex]
So the equation of the parabola is:
[tex]\sf y = -\dfrac12(x - 7)(x - 1)[/tex]
Or in standard form:
[tex]\sf y = -\dfrac12x^2+4x-\dfrac72[/tex]
