Question

URGENT I HAVE ALMOST 0 TIME LEFT I NEED LAST MINUTE HELP

Answer 1

Answer:

The zeros are the points where the parabola intercepts the x-axis.

$\sf x = 7 \implies x - 7 = 0$

$\sf x = 1 \implies x - 1 = 0$

$\sf \implies y = a(x - 7)(x - 1)$  where a is some constant

If the parabola passes through point (3, 4) then:

$\sf \implies a(3 - 7)(3 - 1) = 4$

$\sf \implies a(-4)(2) = 4$

$\sf \implies -8a = 4$

$\sf \implies a = -\dfrac12$

So the equation of the parabola is:

$\sf y = -\dfrac12(x - 7)(x - 1)$

Or in standard form:

$\sf y = -\dfrac12x^2+4x-\dfrac72$