Question

Describe the set of values less than or equal to those represented by a quadratic function with vertex (–10, –25) and containing the point (−16, -17 4/5).

Answer 1

The set of values less than or equal to those represented by a quadratic function with a given vertex and point can be found by finding the equation of the quadratic function and substituting different x values to check the corresponding y values.

Step-by-step explanation:

The quadratic function with vertex (-10, -25) can be written in the form f(x) = a(x-h) ^2 + k, where (h,k) is the vertex.

So, the equation of the quadratic function is f(x) = a (x + 10) ^2 - 25.

Since the function contains the point (-16, -17 4/5), we can substitute the x and y coordinates into the equation to find the value of a.

Using the equation -17 4/5 = a (-16 + 10) ^2 - 25, we can solve for a and find the value of a = -1/10.

Now that we have the equation of the quadratic function, we can find the set of values less than or equal to it by substituting different values of x and checking if the corresponding y value is less than or equal to the y value of the function.