Quadratic Functions X- and Y-Intercepts

Questions and Answers

How do you find the y-intercept of a graph?

Use x = 0 and solve for y in the equation.

What is the calculator shortcut to finding the y-intercept of a function?

[y=] Type in the function, [2nd][Calc][Value], under x =, type in 0.

How do you find the roots/x-intercepts/zeros of a parabola graphically?

Set y = 0 and solve for x, usually by factoring.

What is the calculator shortcut to finding the x-intercepts of a function?

[y=] Type in the function, [2nd][Calc][Zero], for left and right bounds, and guess. Signup and view all the answers

Convert the following quadratic equation into intercept form and find the zeros: y = 2x² - 3x - 2.

y = (x - 2)(2x + 1), zeros at {-1/2, 2}. Signup and view all the answers

What is the formula for the sum of the roots of a parabola?

sum of the roots = -b/a. Signup and view all the answers

What is the formula for the product of the roots of a parabola?

product of the roots = c/a. Signup and view all the answers

What is the quadratic formula and when is it used?

x = [-b ± √(b² - 4ac)] / (2a), used when factoring is not possible. Signup and view all the answers

How do you find where a quadratic function intersects another function?

Solve it like a system of equations. Signup and view all the answers

Study Notes

Y-Intercepts

Y-intercept occurs where the graph intersects the y-axis, found by setting x = 0 in the equation.
For the equation y = 2x² - 3x - 2, substituting x = 0 gives y = -2.
Calculator shortcut for y-intercept: Input the function, then access the calculation menu to evaluate at x = 0.

X-Intercepts (Roots/Zeros)

X-intercepts are the points where the graph crosses the x-axis, determined by setting y = 0 and solving for x.
For the equation y = x² + 5x + 6, factoring leads to (x + 2)(x + 3) = 0, resulting in roots x = -2 and x = -3.

Finding X-Intercepts with a Calculator

To find x-intercepts using a calculator, input the function, then select the zero calculation option.
Define left and right bounds around the zero and guess the location of the zero for accurate results.

Factoring Quadratic Expressions

To factor a quadratic such as y = 2x² - 3x - 2, compute a * c (product of the leading coefficient and constant) and identify factors that sum to b.
In y = 2x² - 3x - 2, the factors of -4 that add to -3 are -4 and +1, allowing the expression to be factored as (x - 2)(2x + 1).

Zeros of a Quadratic Function

The zeros of a quadratic function can be found in intercept form by setting y = 0 and solving the factored equation.
For y = (2x + 1)(x - 2), the zeros are found at x = -1/2 and x = 2.

The sum of the roots of a parabola is given by the formula: sum = -b/a.
The product of the roots is calculated using: product = c/a.

Quadratic Formula

The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a), applicable when factoring is not feasible.
In this formula, a, b, and c represent coefficients from the standard quadratic form y = ax² + bx + c.

Intersection of Quadratic Functions

To find intersection points between a quadratic function and another function, treat the situation as a system of equations and solve accordingly.

Description

Test your understanding of finding the x- and y-intercepts of quadratic functions. This quiz features flashcards that guide you through the process of determining intercepts using the example function y = 2x² - 3x - 2. Hone your skills and deepen your comprehension of quadratic graphs!