Trigonometry and Quadratic Functions Quiz
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Questions and Answers

Find the measure of each side indicated. Round to the nearest tenth.

10.6

  1. Domain:

Range:

Domain: -2, 0, 1

Range: -1, 2, 4

Write in vertex form or graphing form.

  1. y = x^2 + 2x - 3

y = (x + 1)^2 - 4

Write in vertex form or graphing form.

  1. y = x^2 + 10x + 16

<p>y = (x + 5)^2 - 9</p> Signup and view all the answers

Evaluate each function.

  1. f(n) = 4n + 2; Find f(-5)

<p>-18</p> Signup and view all the answers

Flashcards

Domain

The set of all possible x-values (inputs) for a function or graph.

Range

The set of all possible y-values (outputs) for a function or graph.

Vertex Form

A way of writing a quadratic function that shows the vertex, which is the turning point of the parabola.

Graphing Form

A way of rewriting a quadratic equation into the form y = a(x - h)2 + k, where ( h, k ) is the vertex.

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Evaluating a Function

Finding the value of a function for a specific input value.

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Solving for an Input Value

A method of finding a specific input value that makes a function equal to a given output value.

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Linear Equation

An equation that can be written in the form ax + b = c, where a, b, and c are constants.

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Substitution Method

A method for solving a system of linear equations, where you isolate one variable in one equation and substitute it into the other equation.

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Elimination Method

A way of solving a system of equations by eliminating one variable using multiplication and addition/subtraction.

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Logarithm

The inverse of an exponential function, which relates the exponent to the base and the result.

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Base of a Logarithm

The base of the logarithm indicates the power to which the base must be raised to obtain the result.

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Identity Function

A function that takes a number as input and returns the same number as output.

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Radical Form

A mathematical expression containing a radical, which represents a root.

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Exponential Form

A mathematical expression that uses exponents to represent roots, fractions, and powers.

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Study Notes

Problem 1

  • Find the measure of side x.
  • Side AB = 8
  • Angle A = 41°
  • Angle C = 90°
  • Use the trigonometric ratios.
  • Find side x using the sine rule

Problem 2

  • Find the measure of side x.
  • Side AB = 5
  • Angle A = 42°
  • Angle C = 90°
  • Use the trigonometric ratios.
  • Find side x using the cosine rule

Problem 3

  • Domain: All real numbers
  • Range: y ≤ 2

Problem 4

  • Domain: All real numbers
  • Range: y ≤ 4

Problem 5

  • Write the equation in vertex form
  • y = x² + 2x - 3

Problem 6

  • Write the equation in vertex form
  • y = x² + 10x + 16

Problem 7

  • f(n) = 4n + 2
  • Find f(-5)
  • Substitute n = -5 into the equation
  • f(-5) = 4 * (-5) + 2
  • f(-5) = -18

Problem 8

  • f(x) = (x + 4)² − 6
  • Find f(x) when f(x) = 3
  • Substitute f(x) = 3 into the equation
  • 3 = (x + 4)² − 6

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Description

Test your understanding of trigonometric ratios and quadratic equations with this comprehensive quiz. Solve problems using the sine and cosine rules, and convert equations into vertex form. Perfect for students looking to reinforce their math skills.

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