given the quadratic function f(x)
4x^2 -24x +36 find the value of x such that f(x)=4
just solve
4x^2 -24x +36 = 4
4x^2 - 24x + 32 = 0
x^2 - 6x + 8 = 0
(x-4)(x-2) = 0
looks like there are two values for x.
To find the value of x such that f(x) = 4, we need to solve the quadratic equation 4x^2 - 24x + 36 = 4.
Step 1: Subtract 4 from both sides of the equation to get 4x^2 - 24x + 36 - 4 = 0.
Simplifying this gives 4x^2 - 24x + 32 = 0.
Step 2: Divide the equation by 4 to simplify it further. This yields x^2 - 6x + 8 = 0.
Step 3: Factoring the quadratic equation will help us solve for x. We need to find two numbers that multiply to give us 8 and add up to -6.
The factors of 8 are: 1, 2, 4, 8
Testing the factors, we see that 2 and 4 add up to -6.
Step 4: Rewrite the equation using the factored form:
(x - 2)(x - 4) = 0
Step 5: Set each factor equal to zero and solve for x.
x - 2 = 0 or x - 4 = 0
Solving these equations gives us two possible values of x:
x = 2 or x = 4
Therefore, the values of x such that f(x) = 4 are x = 2 and x = 4.