Write an equation for a quadratic function with the x-intercepts of 5 and 12 and the parabola opens up

Answer 1

Hi Grant H

Since you are given roots for your quadratic, using the factored form of the equation easily applies directly. That said, I recommend that you look up the factored form, since there can be more than one representation.

I will give two below

y = a(x - r)(x - s), where r and s represent the roots and any positive value of a will result in a parabola that opens up

y = a(x - p)(x - q), where p and q represent the roots and any positive value of a will result in a parabola that opens up

So there are many equations that fit and if you graph them on the same grid you can confirm that they have the same zeros

when a is positive all these work

y = 1(x-5)(x-12) = x² -17x + 60

y = 2(x-5)(x-12) = 2x² -34x + 120

y = (1/2)(x-5)(x-12) = 0.5x² - 8.5x + 30

You can graph all these at desmos.com on the same grid to see the x intercepts, also you should look up and review the different formats of the Quadratic Equation. The Standard Form, Vertex Form and Factored Form(also call Slope Intercept Form) contain different variables and it is good see how they compare and how the formats can be converted to one another.

I hope this helps

Answer 2

When writing the equation of a quadratic function given its roots, we are able to write it in factored form, which would look like (x-a)(x-b), where "a" and "b" are the given x-intercepts of the function.

Since we have 5 and 12 as our roots, the equation in factored form is simply (x-5)(x-12).

Now, this parabola opens up, which means that what we currently have is accurate. If it were to open down, we would simply negate what we have and move on.

Using FOIL (First, Outer, Inner, Last), we get x²-12x-5x+60.

Combining like terms, we get the solution: x²-17x+60

Answer 3

If the x-intercepts are 5 and 12, then (x-5) and (x-12) are factors. So the equation

y=(x-5)(x-12) satisfies the condition. If we "FOIL" this out to put it in standard form, we get:

y = x^2 -12x - 5x + 60 = x^2-17x+60

The general form is y=ax^2+bx+c, and it opens upward whenever a>0. Here, a=1, so the condition is satisfied, so that's our final answer: x^2-17x+60