Final answer:
To write the quadratic function y = 3x² + 10x in vertex form, we need to complete the square. The correct vertex form is y = 3(x - 5) ² + 10.
Step-by-step explanation:
To write the quadratic function y = 3x² + 10x in vertex form, we first need to complete the square.
Step 1: Factor out the coefficient of x² from the equation.
y = 3(x² + 10/3x)
Step 2: Take half of the coefficient of x and square it.
Half of 10/3 is 5/3, and squaring it gives us 25/9.
Step 3: Add the squared value from step 2 inside the parentheses and subtract the same value multiplied by the coefficient of x outside the parentheses.
y = 3(x² + 10/3x + 25/9) - 3(25/9)
Step 4: Simplify the expression inside the parentheses.
y = 3(x + 5/3) ² - 25/3
The equation y = 3(x + 5/3) ² - 25/3 is in vertex form.
Comparing the given options with the derived equation, we can see that the correct vertex form is option C: (y = 3(x - 5) ² + 10).