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y-Intercepts a2 level

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y-Intercepts a2 level

Study Guide

Key Definition

The y-intercept of a function is the point where the graph intersects the y-axis. To find it, set $x = 0$ in the equation and solve for $y$.

Important Notes

The y-intercept is a point $(0, y)$ on the graph.
For the equation $y = ax^2 + bx + c$, the y-intercept is $c$.
Using y-intercepts helps in graphing functions quickly.
In real-world scenarios, y-intercepts can represent starting values.

Mathematical Notation

$\frac{a}{b}$ represents a fraction

$+$ represents addition

$x^2$ represents x squared

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

Remember to use proper notation when solving problems

Why It Works

Finding the y-intercept by setting $x = 0$ works because it directly gives the value where the graph crosses the y-axis.

Remember

For any linear equation $y = mx + b$, the y-intercept is $b$.

Quick Reference

Y-intercept Formula:$y = f(0)$

Understanding y-Intercepts a2 level

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Video explanation of this concept

Beginner

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Beginner Explanation

For a linear equation $y = mx + b$, the y-intercept is the point (0, b). Setting $x = 0$ gives $y = b$. For example, for $y = 3x + 4$, the y-intercept is (0, 4).

Practice Problems

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Quick Quiz

Single Choice Quiz

Beginner

What is the y-intercept of $y = 3x + 4$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A skateboard ramp’s height can be modeled by $y = -0.5x^2 + 2x + 3$. What is the y-intercept?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the y-intercept of $y = x^3 - 4x + 5$.

Challenge Quiz

Single Choice Quiz

Advanced

Find the y-intercept of $y = 2x^3 - 6x^2 + 4x - 8$.

Recap

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Review key concepts and takeaways