Question

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

A parabola has zeros of 7 and 1 and passes through the point (3,4). Determine the equation of the parabola.

Answer 1

Spot the quadratic equation:-

• (x-1)(x-7)
• x(x-7)-1(x-7)
• x²-7x-x+7
• x²-8x+7

Find a through (3,4)

• a(x²-8x+7)=4
• a(9-24+7)=4
• a(-8)=4
• a=-1/2

Equation:-

• y=-1/2(x-7)(x-1)

Answer 2

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 = -\frac12`

So the equation of the parabola is:

`\sf y = -\frac12(x - 7)(x - 1)`

Or in standard form:

`\sf y = -\frac12x^2+4x-\frac72`