Intercepts and Simplifying Radicals. Learn how to find x-intercepts and y-intercepts algebraically, simplify square-root radicals with numerical and variable radicands, and rationalize denominators so no radical remains in the bottom of a fraction.
Introduction to Quadratic Functions. Discover the three forms of a quadratic function, learn why every quadratic graph is a parabola, and practise finding x-intercepts and y-intercepts for quadratics in standard, factored, and vertex form.
Solving Quadratic Equations Graphically. Understand the difference between a quadratic function and a quadratic equation, then use a graphing calculator to find roots by locating x-intercepts. Explore the three possible outcome cases: two distinct roots, one double root, or no real roots.
The Square Root Principle. Master the square root principle, isolate a squared expression, take both the positive and negative root, and solve. Apply the principle to solve quadratic equations exactly, including cases that require rationalizing.
Inside the lesson: a free preview
What Are Intercepts?
Definition: Intercepts. The x-intercept is the point where the graph crosses the x-axis.
The y-intercept is the point where the graph crosses the y-axis.
Finding Intercepts Algebraically
The Two Rules.
Why does this work? On the x-axis, the y-coordinate is always 0. On the y-axis, the x-coordinate is always 0. So substituting 0 for one variable finds the exact point where the graph meets that axis.
Simplifying Radicals: What Does Simplest Form Mean?
A radical (square root) is in simplest form when the number inside, called the radicand, contains no perfect square factors.
Perfect squares are numbers that come from squaring a whole number:
Worked example: Find the Intercepts of y = 3x + 6
Finding the x-intercept, set y = 0:
Step 1: Start with the given equation. y = 3x + 6
Step 2: Replace y with 0. 0 = 3x + 6
Step 3: Subtract 6 from both sides. -6 = 3x
Step 4: Divide both sides by 3. x = -2
The x-intercept is (-2, 0).
Finding the y-intercept, set x = 0:
Step 1: Start with the given equation. y = 3x + 6
Step 2: Replace x with 0. y = 3(0) + 6
Step 3: Simplify. y = 6
The y-intercept is (0, 6).
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.