Given the quadratic function f(x) = x2 – 18x + 81, find a value of x such that f(x) = 16.
Solve the equation
x^2-18x+81=16
x^2-18x+65=0
f(x) = x^2 – 18x + 81
f(x) = 16
substituting the value of f(x) to the quadratic equation,
16 = x^2 - 18x + 81
0 = x^2 - 18x + 81 - 16
0 = x^2 - 18x + 65
0 = (x-13)(x-5)
thus,
x = 13 and x = 5
hope this helps~ :)
To find the value of x such that f(x) = 16, we need to solve the quadratic equation x^2 - 18x + 81 = 16.
Step 1: Rewrite the equation as a quadratic equation by subtracting 16 from both sides:
x^2 - 18x + 81 - 16 = 0
x^2 - 18x + 65 = 0
Step 2: Factorize the quadratic equation or use the quadratic formula to solve for x.
We can factorize the equation: (x - 13)(x - 5) = 0
Setting each factor equal to zero, we get:
x - 13 = 0 => x = 13
x - 5 = 0 => x = 5
Therefore, there are two possible values of x that satisfy the equation f(x) = 16: x = 13 and x = 5.