Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32)?

Or, in standard form:

Step-by-step explanation:

We can use the factored form of a quadratic equation:

Where a is the leading coefficient and p and q are the zeros of the quadratic.

We know that the x-intercepts are at (2, 0) and (-7, 0).

So, let's substitute 2 for p and -7 for q. This yields:

Now, we need to determine a.

We know that it passes through the point (1, 32). In other words, if we substitute 1 for x, we should get 32 for f(x). Therefore:

We can now solve for a. First, compute:

Multiply:

Divide both sides by -8:

So, the value of a is -4.

Therefore, our entire equation is:

Notes:

We can expand this into standard form:

ci

step-by-step explanation:

answer: what equations are there

step-by-step explanation: