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Questions and Answers
The standard form of a quadratic equation is ax² + bx + ______ = 0
The standard form of a quadratic equation is ax² + bx + ______ = 0
c
In a system of equations, an independent system has ______ solution(s).
In a system of equations, an independent system has ______ solution(s).
one
Functions are often evaluated using function ______.
Functions are often evaluated using function ______.
notation
A quadratic equation can have ______ solutions, which can be real or imaginary.
A quadratic equation can have ______ solutions, which can be real or imaginary.
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When graphing, a ______ transformation reflects the graph across an axis.
When graphing, a ______ transformation reflects the graph across an axis.
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The ______ behavior of a graph refers to how the graph behaves as the inputs approach infinity.
The ______ behavior of a graph refers to how the graph behaves as the inputs approach infinity.
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The discriminant of a quadratic is found using the formula b² - 4ac. It helps determine the ______ of the solutions.
The discriminant of a quadratic is found using the formula b² - 4ac. It helps determine the ______ of the solutions.
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A piecewise function is defined by different ______ over various intervals.
A piecewise function is defined by different ______ over various intervals.
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Study Notes
Solving Systems of Equations by Graphing
- Systems of equations are sets of two or more equations with the same variables.
- Independent systems have exactly one solution.
- Dependent systems have infinite solutions.
- Inconsistent systems have no solution.
- Consistent systems have at least one solution.
Function Notation
- Function notation is a way to write equations that represent functions.
- Common notations include f(x), g(x), or h(x).
End Behavior of Graphs of Functions
- End behavior describes the behavior of a graph as it approaches positive or negative infinity.
- At the right end, the values of y increase or decrease.
- At the left end, the values of y increase or decrease.
Piecewise Functions
- Piecewise functions are functions that include two or more expressions.
- A break in a piecewise graph uses a dot to indicate a included point.
- A circle on a piecewise graph indicates a point that is not included.
Graphing Quadratic Functions
- The zero of a function is located at the x-intercept.
- To graph find the $x$-intercept (solution) on a calculator:
- Enter the related function
- Press graph
- Press 2nd, trace
- Press 2:zero
- Left bound and Enter
- Right bound and Enter
- Guess and Enter
- Solving quadratic equations by graphing related functions.
Quadratic Equations
- The solution of an equation is the value of the variable that makes the equation true.
- Quadratic equations are equations in the form ax² + bx + c=0.
- The standard form is ax² + bx + c=0.
- The discriminant of a quadratic equation is b²-4ac.
- b² - 4ac > 0, two real solutions
- b² - 4ac = 0, one real solution
- b² - 4ac < 0, no real solutions, two imaginary solutions.
Factoring Polynomials
- Factoring is the process of finding the factors of a polynomial.
- Different types of polynomials include: difference of squares, sum of squares, and perfect square trinomials.
Solving Quadratic Equations by Completing the Square
- To solve a quadratic equation by completing the square, follow these steps:
- Write the quadratic equation in the form x² + bx = c
- Find (b/2)² and add the value to both sides of the equation
- Write the left side as a factor.
- Solve by taking the square root of both sides.
- If a ≠ 1, divide every term of the equation by a
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Description
This quiz covers essential topics of algebra including solving systems of equations by graphing, function notation, and end behavior of graphs. Additionally, it delves into piecewise functions and how to graph quadratic functions. Test your understanding of these key concepts and their applications in algebra.
