Mini-Lecture 9.5: Graphing Quadratic Equations | Montgomery College - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

194

Pages:

1
Author:

Alvin Bradford

Mini-Lecture 9.5 Graphing Quadratic Equations Learning Objectives: 1. Graph quadratic equations of the form y = ax 2 . 2. Graph quadratic equations of the form y = ax 2 + bx + c . 3. Use the vertex formula to determine the vertex of a parabola. Examples: 1. Graph each quadratic equation by finding and plotting ordered pair solutions. a) y = x 2 b) y = 4 x 2 c) y = −2 x 2 2. Sketch the graph of each equation. Label the vertex and the intercepts. a) y = x 2 − 4 d) b) y = x 2 + 16 y = x 2 + 7 x + 10 g) y = 1 2 x 5 c) y = − x2 − 2 y = − x2 + 6 x − 9 e) y = − x2 + x + 6 f) h) y = x2 + 5x i) y = −2 x 2 + 5 x − 3 Teaching Notes: • • • • Remind students that a parabola is a smooth curve; not a point. Encourage students to always find the x- and y-intercepts, if they exist. Most students prefer graphing by vertex and intercepts rather than by finding points. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) – 2i) see mini-lecture graphing answers; 2a) V=(0,-4), (2, 0), (-2, 0); 2b) V=(0, 16); ⎛ 7 ⎝ 2 9⎞ 4⎠ ⎛ 1 25 ⎞ ⎟ , (0, 6), (-2,0), (3,0); ⎝2 4 ⎠ ⎛ 5 25 ⎞ ⎛ 5 1⎞ , (0, 0), (-5, 0); 2i) V= ⎜ , ⎟ , (1, 0), (3/2, 0), (0, -3) 2f)V = (3, 0), (0, -9); 2g) V=(0, 0); 2h) V= ⎜ − , − ⎟ 4 ⎠ ⎝ 2 ⎝ 4 8⎠ 2c) V = (0,-2); 2d) V= ⎜ − , − ⎟ , (-2, 0), (-5, 0), (0, 10); 2e) V= ⎜ ,

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