Math Problem Statement

Y= (x+5)2 +9

Solution

The given equation is:

y=(x+5)2+9y = (x + 5)^2 + 9

This is a quadratic function in the standard form of a parabola, y=a(xh)2+ky = a(x-h)^2 + k, where:

  • a=1a = 1 (the coefficient of (x+5)2(x + 5)^2),
  • h=5h = -5 (the x-coordinate of the vertex, derived from x+5=0x + 5 = 0),
  • k=9k = 9 (the y-coordinate of the vertex).

Key points:

  • Vertex: The vertex is at (5,9)(-5, 9). This is the point where the parabola reaches its minimum value since a>0a > 0, which means it opens upwards.
  • Axis of symmetry: The axis of symmetry is the vertical line x=5x = -5.
  • Direction: The parabola opens upwards because a=1>0a = 1 > 0.

Let me know if you'd like more details about this equation, or if you have any specific questions!

Follow-up questions:

  1. How can we find the x-intercepts of this equation?
  2. What happens if we change the value of aa?
  3. How do you graph a quadratic function from its vertex form?
  4. How do you calculate the maximum or minimum value of a quadratic function?
  5. Can you solve this equation for a specific value of yy?

Tip:

When working with vertex form y=a(xh)2+ky = a(x-h)^2 + k, you can directly identify the vertex, axis of symmetry, and direction of the parabola, making it easier to sketch the graph!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex Form of a Parabola

Formulas

Vertex form of a quadratic function: y = a(x - h)^2 + k

Theorems

Vertex form of a parabola
Properties of parabolas

Suitable Grade Level

Grades 8-10