Alg 1 STAAR Review

Front

What is the power of a power property in exponents?

Back

When raising a power to another power, multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

What is the definition of a function's vertex?

Back

The vertex of a function is the highest or lowest point on the graph of a quadratic function, represented as \( (h, k) \) in the vertex form \( y = a(x-h)^2 + k \).

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function \( g(x) \) at a specific value, substitute the value into the function: \( g(20) = 6(2(20) + 7) \).

Front

What is the formula for the slope of a line?

Back

The slope \( m \) of a line is calculated as \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation \( x = h \) where \( h \) is the x-coordinate of the vertex.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is \( Ax + By = C \), where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

Front

How do you find the zeros of a function?

Back

To find the zeros of a function, set the function equal to zero and solve for the variable: \( f(x) = 0 \).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation \( ax^2 + bx + c = 0 \): \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( b^2 - 4ac \) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.