Math Problem Statement

Use a graph to solve each equation and inequality: 1. -x + 2 = x^2 2. (1/4) |x + 3| = 2 3. x^2 + 2x - 3 > 0 4. x^2 - 7x - 8 < 0

Solution

The image contains a set of math problems under "Practice & Problem Solving," which involve solving equations and inequalities using a graph. The problems are:

Solve each equation using a graph:

  1. x+2=x2-x + 2 = x^2
  2. 14x+3=2\frac{1}{4} |x + 3| = 2

Solve each inequality using a graph:

  1. x2+2x3>0x^2 + 2x - 3 > 0
  2. x27x8<0x^2 - 7x - 8 < 0

Would you like step-by-step solutions or explanations on how to solve them using graphs?

Here are five related questions to deepen understanding:

  1. How do you determine the points of intersection between a quadratic equation and a linear equation graphically?
  2. What role does the vertex of a quadratic function play in solving inequalities?
  3. How do you graph an absolute value function and interpret its solutions?
  4. What does the solution set of a quadratic inequality represent in a graph?
  5. How can factoring help solve quadratic inequalities without graphing?

Tip: When solving equations graphically, plot both sides as separate functions and find their intersection points!

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Math Problem Analysis

Mathematical Concepts

Graphing Equations
Quadratic Equations
Absolute Value Equations
Inequalities

Formulas

Quadratic equation: ax^2 + bx + c = 0
Vertex form of a quadratic: y = a(x - h)^2 + k
Absolute value function: y = a|x - h| + k

Theorems

Intersection Method for Solving Equations Graphically
Zero Product Property
Sign Analysis for Quadratic Inequalities

Suitable Grade Level

Grades 8-10