Quadratic Functions X- and Y-Intercepts

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.

Formulas Related to Roots

• 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.

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!