Determine the equation of the quadraticcc function
f(x)=ax^2-6x-7 if f(2)=3
we substitute the given values and solve for a. at x = 2, f(x) = 3:
3 = a(2^2) - 6(2) - 7
3 = 4a - 12 - 7
3 = 4a - 19
3 + 19 = 4a
22 = 4a
a = 5.5
substituting back,
f(x) = 5.5x^2 - 6x - 7
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Well, we know that f(2) = 3. Let's substitute these values into the equation:
3 = a(2^2) - 6(2) - 7
Simplifying, we get:
3 = 4a - 12 - 7
Combine like terms:
4a - 19 = 3
Add 19 to both sides:
4a = 22
Divide both sides by 4:
a = 22/4
Simplifying further:
a = 11/2
So, the equation of the quadratic function is:
f(x) = (11/2)x^2 - 6x - 7
To determine the equation of the quadratic function, we will use the given information that f(2) = 3.
Step 1: Substitute the value of x and f(x) into the equation:
3 = a(2)^2 - 6(2) - 7
Step 2: Simplify the expression:
3 = 4a - 12 - 7
3 = 4a - 19
Step 3: Rearrange the equation to solve for a:
4a = 3 + 19
4a = 22
Step 4: Divide both sides of the equation by 4 to isolate a:
a = 22/4
a = 5.5
Step 5: Substitute the value of a back into the original equation to get the final equation of the quadratic function:
f(x) = 5.5x^2 - 6x - 7
Therefore, the equation of the quadratic function f(x) is f(x) = 5.5x^2 - 6x - 7.