Hi, I am looking for the x coordinates only..f(x)= -x^2 + 2x + 15
Thanks..
factor it and solve ;
what i do is ignore the negative in front of the x^2 for now
giving you x^2 + 2x +15
take 1x from the x^2 and multiply it with the 15 giving you 15x. now figure out which to numbers multiply to make 15 (there is only 1 x 15, and 3 x 5) out of these two which can be added to make a 2 (because of the 2x)your answer would be 3 and 5 if one was a negative but we wont put a negative in front of them because the origional equation had the x^2 as a negative so that changes the problem a little.
so now you should have a factor out equation which is (x+ 5 and -x+ 3) one of the x is negative because the x^2 was negative now just put both equation equal to zero and solve for x you should get;
x= -5, and 3 now put it back into original polynomial and whichever one doesnt equal zero wont be an answer
You can't just ignore one - sign. It's easier to have the leading coefficient be positive, so multiply the whole equation by -1 to get
x^2 - 2x - 15 = 0
(x-5)(x+3) = 0
so, x = 5,-3
To find the x-intercepts, which are the x-coordinates where the function intersects or crosses the x-axis, we need to solve the equation f(x) = -x^2 + 2x + 15 for x when f(x) equals 0.
So, set the equation equal to 0:
0 = -x^2 + 2x + 15
Next, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In the quadratic equation ax^2 + bx + c = 0, we have:
a = -1, b = 2, and c = 15.
Substituting these values into the quadratic formula:
x = (-2 ± √(2^2 - 4(-1)(15))) / 2(-1)
Simplifying:
x = (-2 ± √(4 + 60)) / (-2)
x = (-2 ± √(64)) / (-2)
x = (-2 ± 8) / (-2)
There are two possible solutions:
x1 = (-2 + 8) / (-2) = 6 / (-2) = -3
x2 = (-2 - 8) / (-2) = -10 / (-2) = 5
Therefore, the x-coordinates or x-intercepts of the function f(x) = -x^2 + 2x + 15 are -3 and 5.