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?
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Convert the following quadratic equation into intercept form and find the zeros: y = 2x² - 3x - 2.
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What is the formula for the sum of the roots of a parabola?
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What is the formula for the product of the roots of a parabola?
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What is the quadratic formula and when is it used?
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How do you find where a quadratic function intersects another function?
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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.
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.
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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!