Question

Find the equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0)

Answer 1

The equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0) is $y=x^{2}-x-12$

Solution:

We have to find the equation of a parabola that opens up and has the following x intercepts (-3, 0) and (4, 0)

x-intercepts of the parabola are (−3, 0) and (4, 0)

So, we can form an equation:

Also x = 4

x – 4 = 0

x – 4 = 0 is another factor of quadratic equation.

The quadratic function is:

$\begin{array}{l}{y=(x+3)(x-4)} \\\\ {y=x^{2}-4 x+3 x-12} \\\\ {y=x^{2}-x-12}\end{array}$

Hence, the equation of the parabola is  $y=x^{2}-x-12$