Math Problem Statement

f(x)=3x 2 +5x−7

Solution

It looks like you are providing a function, but there's a formatting issue. Let me rewrite the function clearly:

f(x)=3x2+5x7f(x) = 3x^2 + 5x - 7

This is a quadratic function, with the general form:

f(x)=ax2+bx+cf(x) = ax^2 + bx + c

where:

  • a=3a = 3
  • b=5b = 5
  • c=7c = -7

Would you like to explore something specific about this function? For example, I can help you with finding its roots, vertex, or its graph.

Let me know if you need details, and here are five related questions you might consider:

  1. How do you find the roots (solutions) of f(x)=3x2+5x7f(x) = 3x^2 + 5x - 7?
  2. What is the vertex of the quadratic function f(x)=3x2+5x7f(x) = 3x^2 + 5x - 7?
  3. How do you find the axis of symmetry for this quadratic function?
  4. How can we determine the function's minimum or maximum value?
  5. What is the effect of changing the coefficient aa on the shape of the parabola?

Tip: The vertex form of a quadratic function gives you more information about the graph, like the vertex and whether it opens upward or downward!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Functions

Formulas

Quadratic equation formula: ax^2 + bx + c = 0
Vertex formula: x = -b / (2a)
Discriminant formula: Δ = b^2 - 4ac

Theorems

Quadratic Formula
Vertex Theorem
Discriminant Theorem

Suitable Grade Level

Grades 9-10