As with linear equations, the -intercepts of a parabola are where the graph intersects the -axis. The -value is zero at the -intercepts.
leading coefficient of a parabola
The variable in the equation is called the leading coefficient of the quadratic equation.
minimums and maximums of a parabola
An equation of the form forms a parabola.
If is positive, the parabola will open upward. The vertex will be a minimum.
If is negative, the parabola will open downward. The vertex will be a maximum.
symmetry of a parabola
A parabola can be divided in half by a vertical line. Because of this, parabolas have symmetry. The vertical line dividing the parabola into two equal portions is called the line of symmetry.
vertex of a parabola
All parabolas have a vertex, the ordered pair that represents the bottom (or the top) of the curve. The line of symmetry always goes through the vertex. The vertex of a parabola is the ordered pair .
A coefficient is the number in front of a variable.
To reduce or enlarge a figure according to a scale factor is a dilation.
The domain of a function is the set of -values for which the function is defined.
A horizontal shift is the result of adding a constant term to the function inside the parentheses. A positive term results in a shift to the left and a negative term in a shift to the right.
A parabola is the characteristic shape of a quadratic function graph, resembling a "U".
A quadratic function is a function that can be written in the form , where , , and are real constants and .
The standard form of a quadratic function is .
A figure has symmetry if it can be transformed and still look the same.
The vertex of a parabola is the highest or lowest point on the graph of a parabola. The vertex is the maximum point of a parabola that opens downward and the minimum point of a parabola that opens upward.
The vertical axis is also referred to as the -axis of a coordinate graph. By convention, we graph the output variable on the -axis.
Learn the anatomy of the graph of a quadratic function.