write the quadratic function in vertex form:
f(x) = x^2 - 3x - 10
To write the quadratic function in vertex form, we need to complete the square.
Step 1: Take out the common factor (if any)
In this case, there is no common factor we can take out.
Step 2: Rearrange the function to group the x terms together
f(x) = (x^2 - 3x) - 10
Step 3: Complete the square inside the parentheses
To complete the square, we want to take half of the coefficient of the x term, square it, and add it inside the parentheses.
The coefficient of the x term is -3, half of which is -3/2. Squaring -3/2 gives 9/4.
f(x) = (x^2 - 3x + 9/4) - 9/4 - 10
Step 4: Simplify inside the parentheses
f(x) = (x^2 - 3x + 9/4) - 49/4
Step 5: Simplify the constant terms outside the parentheses
f(x) = (x - 3/2)^2 - 49/4
Therefore, the quadratic function in vertex form is f(x) = (x - 3/2)^2 - 49/4.