Unit 8
Glossary
Algebra 1
Completing the square is a method of rewriting a quadratic expression or equation.
- A quadratic expression is rewritten in the form \(a(x+p)^2-q\), where \(a\), \(p\), and \(q\) are constants and \(a\neq0.\)
- A quadratic equation is rewritten in the form \(a(x+p)^2=q\).
A quadratic expression is in factored form when it is written as the product of a constant times two linear factors.
- \(2x^2 + 4x - 6\) written in factored form is \(2(x-1)(x+3)\).
- \(15x^2 + x - 2\) written in factored form is \((5x + 2)(3x-1)\).
An irrational number is a number that is not rational. This means it cannot be expressed as a positive fraction, a negative fraction, or zero. It cannot be written in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).
For example, the numbers \(\pi\) and \(\text{-}\sqrt{2}\) are irrational numbers.
From an earlier course.
A linear term of an expression has a variable raised to the first power.
- In the expression, \(5x+2\), the linear term is \(5x\).
- In the expression, \(20-x^2+x\), the linear term is \(x\).
- In the expression \(ax^2+bx+c\), where \(a\), \(b\), and \(c\) are constants, the linear term is \(bx\).
A perfect square is a number or an expression that is the result of multiplying a number or an expression to itself. In general, the multiplied number is rational and the multiplied expression has rational coefficients.
A quadratic equation is an equation that is equivalent to one of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
The quadratic formula is \(x = {\text-b \pm \sqrt{b^2-4ac} \over 2a}\) and gives the solutions of the quadratic equation \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
A rational number is a number that can be written as a positive fraction, a negative fraction, or zero. It can be written in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).
- 0.7 is a rational number because it can be written as \(\frac{7}{10}\).
- The numbers 0, 3, \(\text{-}\frac{3}{4}\), and 6.7 are all rational numbers.
From an earlier course.
The standard form of a quadratic expression is \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a\) \(\ne\) 0.
A zero of a function is an input that results in an output of 0. In other words, if \(f(a) = 0\), then \(a\) is a zero of \(f\).