Math Problem Statement

can you graph it for me

Solution

Here is the graph of the equation y=34(x+3)(x+7)y = -\frac{3}{4}(x+3)(x+7). The parabola opens downwards, and the roots are at x=3x = -3 and x=7x = -7.

Would you like more details or have any questions?

Here are some questions you might consider asking:

  1. How do you find the vertex of this new parabola?
  2. Can you explain how the coefficient 34-\frac{3}{4} affects the graph's shape?
  3. What is the axis of symmetry for this parabola?
  4. How do you derive the vertex form of a quadratic equation from the factored form?
  5. Can you show the steps to solve for the roots algebraically?

Tip: When comparing different quadratic equations, observe how changes in coefficients and constants impact the graph's shape and position.

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Parabolas

Formulas

Quadratic equation formula ax^2 + bx + c = 0
Vertex form of a quadratic equation

Theorems

Vertex form of a parabola
Axis of symmetry

Suitable Grade Level

Grades 10-12