REI.12 algebra 1

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry 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 = -b/2a.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope of a line from its equation?

Back

In the slope-intercept form y = mx + b, the slope is represented by m.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.