Find the Axis of Symmetry for the Quadratic Expression -5x^2 - 25x

Question

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

f(x)=−5x2−25x f(x)=-5x^2-25x

Video Solution

Solution Steps

00:00 Find the axis of symmetry for the function
00:03 The axis of symmetry is the X value at the vertex point
00:06 The point where if you fold the parabola in half, both halves are identical
00:10 Let's look at the function's coefficients
00:18 We'll use the formula to calculate the vertex point
00:28 We'll substitute appropriate values according to the given data and solve for X at the point
00:47 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given coefficients a a and b b .
  • Step 2: Apply the formula for the axis of symmetry.
  • Step 3: Perform the necessary calculations to find the axis of symmetry.

Now, let's work through each step:
Step 1: The given quadratic function is f(x)=−5x2−25x f(x) = -5x^2 - 25x , so a=−5 a = -5 and b=−25 b = -25 .
Step 2: We'll use the axis of symmetry formula x=−b2a x = -\frac{b}{2a} .
Step 3: Plugging in our values, we get x=−−252×−5=−25−10=−2.5 x = -\frac{-25}{2 \times -5} = -\frac{25}{-10} = -2.5 .

Therefore, the axis of symmetry for the quadratic f(x)=−5x2−25x f(x) = -5x^2 - 25x is x=−212 x = -2\frac{1}{2} .

Answer

x=−212 x=-2\frac{1}{2}

More Questions

Related Subjects

Symmetry in a parabola

Question Types

Symmetry: Axis of symmetry