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Questions and Answers
What is the first step in solving the linear equation $2x + 3 = 11$ for $x$?
What is the first step in solving the linear equation $2x + 3 = 11$ for $x$?
- Add 3 to both sides.
- Multiply both sides by 2.
- Divide both sides by 2.
- Subtract 3 from both sides. (correct)
Which of the following is a valid way to solve the quadratic equation $x^2 + 4x + 4 = 0$?
Which of the following is a valid way to solve the quadratic equation $x^2 + 4x + 4 = 0$?
- Using the quadratic formula. (correct)
- Factoring it as $(x + 2)(x + 2) = 0$. (correct)
- Completing the square yielding $0 = 4$.
- Setting $x^2 = -4$.
What does the function $f(x) = 3x - 1$ output when $x = 2$?
What does the function $f(x) = 3x - 1$ output when $x = 2$?
- 7
- 5 (correct)
- 6
- 8
Which statement about functions is true?
Which statement about functions is true?
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Using the quadratic formula, what is the solution for $2x^2 + 3x - 2 = 0$?
Using the quadratic formula, what is the solution for $2x^2 + 3x - 2 = 0$?
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Study Notes
Linear Equations
- Standard form of a linear equation is ( ax + b = c ).
- Solve for ( x ) by isolating it on one side of the equation.
- Rearranging involves subtracting ( b ) from both sides and then dividing by ( a ).
Quadratic Equations
- A quadratic equation is expressed as ( ax^2 + bx + c = 0 ).
- Solutions can be found using:
- Factoring, when applicable.
- Completing the square method.
- The quadratic formula:
- ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
- The term ( b^2 - 4ac ) is called the discriminant, determining the nature of the roots.
Functions
- A function ( f(x) ) uniquely assigns one output for each specific input ( x ).
- Example of a linear function: ( f(x) = 2x + 3 ).
- In this example, inputting a value for ( x ) yields a corresponding ( f(x) ) value.
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