Math Problem Statement

Determine the axis of symmetry for the quadratic function y = 0.3(x - 8)^2 - 6.5.

Solution

The given quadratic function is y=0.3(x8)26.5y = 0.3(x - 8)^2 - 6.5.

This is written in vertex form, y=a(xh)2+ky = a(x - h)^2 + k, where:

  • (h,k)(h, k) is the vertex of the parabola.
  • The axis of symmetry is the vertical line passing through the vertex, which means the equation of the axis of symmetry is x=hx = h.

In this case:

  • h=8h = 8, so the axis of symmetry is x=8x = 8.

Would you like further details or have any questions? Here are some additional questions to expand on this:

  1. How do you find the vertex of a quadratic function in standard form?
  2. How does the value of aa affect the graph of a quadratic function?
  3. What is the significance of the axis of symmetry in a quadratic function?
  4. Can the axis of symmetry ever be negative?
  5. How would you convert a quadratic function from standard form to vertex form?

Tip: The coefficient aa affects the direction of the parabola (whether it opens up or down) and its width.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex Form

Formulas

y = a(x - h)^2 + k

Theorems

Axis of Symmetry Theorem for Quadratic Functions

Suitable Grade Level

Grades 8-10