# Find the real zeros of f. (Enter your answers as a comma-separated list.)

f(x) = −x2 + 7x + 8x

X =_____

Find the x-intercepts of the graph of f.
(x, y) =_______(smaller x-value)
(x, y) =_______(larger x-value)

## You want f(x) to be zero, so

-x^2 + 7x + 8x = 0

I suspect a type, why would you not just add 7x and 8x ?

## To find the real zeros of the polynomial function f(x) = -x^2 + 7x + 8x, we need to set f(x) equal to zero and solve for x.

First, rewrite the function in standard form by combining like terms: f(x) = -x^2 + 15x.

Now, set f(x) equal to zero: -x^2 + 15x = 0.

Next, factor out x: x(-x + 15) = 0.

From this, we can see that either x = 0 or -x + 15 = 0.

Solving the first equation, x = 0.

For the second equation, add x to both sides: -x + 15 + x = x + 15.

Simplifying, 15 = x + 15.

Subtracting 15 from both sides, x = 0.

Therefore, the real zeros of f are x = 0.

To find the x-intercepts of the graph, we need to find the points on the graph where the y-coordinate is equal to zero.

For the given function f(x) = -x^2 + 15x, we can calculate the x-intercepts by setting f(x) equal to zero and solving for x.

Starting with the equation -x^2 + 15x = 0, we can factor out an x: x(-x + 15) = 0.

Thus, either x = 0 or -x + 15 = 0.

Solving the first equation, x = 0.

For the second equation, add x to both sides: -x + 15 + x = x + 15.

This simplifies to 15 = x + 15.

By subtracting 15 from both sides, we get x = 0.

Therefore, the x-intercept of the graph is (0, 0).

So, in summary:
- The real zero of f is x = 0.
- The x-intercept of the graph is (0, 0).