Final answer:
To find a quadratic equation with x-intercepts of -13 and 52, we can use the fact that the x-intercepts occur when the equation equals zero. By setting up two equations and solving them simultaneously, we can find the quadratic equation that satisfies the given conditions.
Step-by-step explanation:
To find a quadratic equation with x-intercepts of -13 and 52, we can use the fact that the x-intercepts occur when the equation equals zero. So, let's assume the quadratic equation is in the form ax^2 + bx + c = 0. The x-intercepts mean that when x = -13 or x = 52, the equation equals zero. Therefore, we have two equations: a(-13)^2 + b(-13) + c = 0 and a(52)^2 + b(52) + c = 0. We can solve these equations to find the values of a, b, and c.
When we solve the first equation, we get 169a - 13b + c = 0. Similarly, solving the second equation gives us 2704a + 52b + c = 0. Now, we have a system of linear equations to solve. By solving these equations simultaneously, we can find the values of a, b, and c, and therefore obtain the quadratic equation that satisfies the given conditions.