Finding A Quadratic Function Using
Muhtasari
A quadratic graph is a smooth U-shaped curve called a parabola, and it is completely fixed by just a few key pieces of information. Tell me its vertex and one more point, or where it crosses the x-axis and one more point, and the whole curve is determined. Working backwards from features to the equation is a powerful and very practical skill.
In this lesson you will find the equation of a quadratic from given information: from its vertex and another point, from its x-intercepts and a point, and from its vertex or x-intercepts in the simple case where the leading coefficient is one. With a couple of standard forms, these problems become straightforward.
Malengo
- given information Find a quadratic function given: (a) vertex and another point (b) x-intercepts and a point (c) vertex or x-intercepts in the case where a = 1.
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- A quadratic has vertex (1, 2) and passes through (3, 10). What is the value of a in y = a(x-1)^2 + 2? A. 1 B. 2 C. 4 D. 8 Answer: B
- A quadratic has roots 2 and 4 and leading coefficient 1. Which is its equation? A. y = (x+2)(x+4) B. y = (x-2)(x-4) C. y = (x-2)(x+4) D. y = 2(x-2)(x-4) Answer: B
- Expanding y = (x-2)(x-4) gives: A. x^2 - 6x + 8 B. x^2 + 6x + 8 C. x^2 - 2x - 8 D. x^2 - 8x + 6 Answer: A
- Which form of a quadratic shows the vertex directly? A. y = ax^2 + bx + c B. y = a(x-p)(x-q) C. y = a(x-h)^2 + k D. y = mx + c Answer: C
- A quadratic has x-intercepts 2 and 4 and passes through (3, -2). What is a in y = a(x-2)(x-4)? A. -2 B. -1 C. 1 D. 2 Answer: D
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Vitabu Vinavyopendekezwa
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Sehemu ya kitabu
Quadratic Functions
Recognize characteristics of parabolas.
"Algebra and Trigonometry: Quadratic Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/5-1-quadratic-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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