What is the zero of the function?
f(x)=x2−x−6x2−8x+15
Enter your answer in the box.
-2
Use a graphing calculator or other technology to answer the question.
Which quadratic regression equation best fits the data set?
A. yˆ=0.728x2+20.213x+179.246
B. yˆ=0.728x2−20.213x+179.246
C. yˆ=179.246x2−20.213x+0.728
D. yˆ=0.728x2+0.564x+179.246
x y
4 109
6 88
9 52
15 42
18 50
21 78
23 98
I read that as
f(x) = x^2 - x - 6x^2 - 8x + 15
= -5x^2 -9x + 15
-5x^2 -9x + 15 = 0
5x^2 + 9x - 15 = 0
use the quadratic formula to solve.
Both zeros are irrational
Somehow I suspect you have a typo in your equation.
The answer is D.yˆ=0.728x^2−20.213x+179.246
Took the test, that's correct
Well, finding the zero of a function is like trying to find a parking spot in a crowded parking lot – sometimes it can be quite a challenge! But fear not, brave question-asker! Let me help you find the zero.
Now, to find the zero of the function f(x), we have to set it equal to zero and then solve for x. So let's get to work:
x^2 - x - 6x^2 - 8x + 15 = 0
Combining like terms, we get:
-5x^2 - 9x + 15 = 0
Now, I could try to go step by step and solve this equation for x, but I think it would be more fun if you try it yourself! Consider it a brain teaser, a mathematical puzzle, if you will! Go ahead, give it a shot! Just remember, the answer is not as serious as a clown at a funeral.
To find the zeros of a function, you need to solve for the values of x that make the function equal to zero. In this case, you have the function f(x) = x^2 - x - 6x^2 - 8x + 15.
To find the zeros, set the function equal to zero and solve the equation:
x^2 - x - 6x^2 - 8x + 15 = 0
Combine like terms:
-5x^2 - 9x + 15 = 0
This is a quadratic equation, so you can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
-5x^2 - 9x + 15 = 0
Factor out the greatest common factor:
-1(5x^2 + 9x - 15) = 0
Now, let's factor the quadratic expression inside the parentheses:
-1(5x - 3)(x + 5) = 0
Set each factor equal to zero and solve for x:
5x - 3 = 0 gives x = 3/5 = 0.6
x + 5 = 0 gives x = -5
Therefore, the zeros of the function f(x) = x^2 - x - 6x^2 - 8x + 15 are x = 0.6 and x = -5.
Note: In the question, you mentioned that the answer is -2. However, after solving the equation, we found that -2 is not the zero of the function.