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Graphing Quadratic Equations using Factoring

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Graphing Quadratic Equations using Factoring

Study Guide

Key Definition

A quadratic equation is a polynomial equation of degree 2. Its standard form is $0 = ax^2 + bx + c$.

Important Notes

The graph of $y = ax^2 + bx + c$ is a parabola.
Factoring helps find the x-intercepts of the parabola.
Use the zero product property: if $(x - p)(x - q) = 0$, then $x = p$ or $x = q$.
The vertex of a parabola is the highest or lowest point.
Always check if a quadratic can be factored before solving by other means.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$x^2$ indicates x squared

$\sqrt{x}$ indicates the square root of x

Remember to use proper notation when solving problems

Why It Works

By factoring the quadratic equation, we can easily find the roots and thus the x-intercepts of the parabola, enabling us to sketch its graph accurately.

Remember

The standard form $0 = ax^2 + bx + c$ is crucial for understanding the properties of the quadratic function.

Quick Reference

Zero Product Property:$(x - p)(x - q) = 0$

Understanding Graphing Quadratic Equations using Factoring

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A quadratic equation has the form $ax^2 + bx + c = 0$. To graph it, we find its x-intercepts by rewriting it in factored form and solving for x, then plot those points and draw the parabola.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is the factored form of $x^2 - 5x + 6 = 0$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a skateboard ramp. The path can be modeled by $y = -x^2 + 4x$. Where will the ramp touch the ground?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the equation $x^2 + 6x + 9 = 0$. Without solving, what can you say about the graph?

Challenge Quiz

Single Choice Quiz

Advanced

Find the vertex of the parabola given by $y = 2x^2 - 8x + 6$.

Recap

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Review key concepts and takeaways