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

Question

Given the expression of the quadratic function

Finding the symmetry point of the function

f(x)=−6x2+24x f(x)=-6x^2+24x

Video Solution

Solution Steps

00:00 Find the point of symmetry in the function
00:03 The point of symmetry is the point where if you fold the parabola in half
00:06 The halves will be equal to each other
00:09 Let's examine the function's coefficients
00:12 We'll use the formula to calculate the vertex point
00:16 We'll substitute appropriate values according to the given data and solve for X at the point
00:27 This is the X value at the point of symmetry
00:30 Now we'll substitute this X value in the function to find the Y value at the point
00:45 This is the Y value at the point of symmetry
00:53 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll find the vertex of the quadratic function f(x)=−6x2+24x 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)=−6x2+24x f(x) = -6x^2 + 24x . Here, a=−6 a = -6 and b=24 b = 24 .
Step 2: Use the vertex formula x=−b2a x = -\frac{b}{2a} . Substituting the values, we get x=−242⋅(−6)=2412=2 x = -\frac{24}{2 \cdot (-6)} = \frac{24}{12} = 2 .
Step 3: Substitute x=2 x = 2 back into the function to find the y-coordinate: f(2)=−6(2)2+24⋅2=−24+48=24 f(2) = -6(2)^2 + 24 \cdot 2 = -24 + 48 = 24 .

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

Answer

(2,24) (2,24)

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Symmetry in a parabola

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