Calculate the Vertex of the Quadratic Function: f(x) = -6x^2 + 24x

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=-6x^2+24x$

To solve this problem, we'll find the vertex of the quadratic function $f(x) = -6x^2 + 24x$.

• Step 1: Identify the coefficients from the quadratic function.
• Step 2: Use the vertex formula to find the x-coordinate.
• Step 3: Substitute the x-coordinate back into the function to find the y-coordinate.

Now, let's work through each step:
Step 1: The function given is $f(x) = -6x^2 + 24x$. Here, $a = -6$ and $b = 24$.
Step 2: Use the vertex formula $x = -\frac{b}{2a}$. Substituting the values, we get $x = -\frac{24}{2 \cdot (-6)} = \frac{24}{12} = 2$.
Step 3: Substitute $x = 2$ back into the function to find the y-coordinate: $f(2) = -6(2)^2 + 24 \cdot 2 = -24 + 48 = 24$.

Therefore, the symmetry point of the function is $(2, 24)$.