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 ?
waiting for your correction.....
jhhi
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).