Quadratic Vocabulary Words to graph by…
Quadratic Function A function that can be written in the standard form y = ax 2+bx+c where a does not equal zero. ¢ The U-shaped graph of a quadratic function is called a parabola ¢
Vertex Form ¢ A quadratic written in the form y = a(x-h)2 + k
Domain The x-values for a function ¢ In quadratics, it is always “all real numbers” or “x > 0” ¢
Range All y-values for a function. ¢ In quadratics, if a is positive, it is “y > the y value of the vertex”, if a is negative, it is “y < the y value of the vertex”. ¢
Vertex ¢ The lowest or highest point on a parabola
Axis of Symmetry ¢ The vertical line that divides the parabola into mirror images and passes through the vertex.
X-intercept The places where the parabola crosses the x-axis. ¢ Graph it and see ¢ Set the function equal to zero and solve for x (there will likely be two solutions) ¢ Aka: roots, zeros, and solutions ¢
y-intercept The places where the parabola crosses the y-axis. ¢ Graph it and see ¢ Set the x’s in the function equal to zero and solve for y (there will always be exactly one) ¢
Interval of increase The places where the y values are increasing as the x values increase. ¢ Always in terms of the x values and read from left to right ¢
Interval of decrease The places where the y values are decreasing as the x values increase. ¢ Always in terms of the x values and read from left to right ¢
Intervals of Increase and Decrease example ¢ ¢ ¢ You can see from the graph that as you move from left to right the value of the function decreases on the left side of the vertex and increases on the right side of the vertex. Increases over x > - ½ Decreases over x < - ½
Maximum value The highest spot on a graph in a localized area ¢ Looks like the “top of the mountain” on a graph that opens down. ¢ Only occurs where a<0 for a quadratic function ¢
Minimum value The lowest spot on a graph in a localized area ¢ Looks like the “bottom of a valley” on a graph that opens up. ¢ Only occurs where a>0 for a quadratic function ¢
Minimum and Maximum value ¢ For a quadratic in standard form, the vertex’s y-coordinate is the minimum value or its maximum value of the function.
Extrema ¢ Extrema are the minimum(s) and maximum(s) of a function on a certain interval.
Positive ¢ Where the a value is greater than zero and the parabola opens up.
Negative ¢ Where the a value is less than zero and the parabola opens down.
Symmetries ¢ A parabola is symmetrical about the axis of symmetry and is an even function when the axis od symmetry is x=0.
End Behavior As x ∞, f(x) _______ ¢ As x approaches infinity, the function approaches _____. ¢ As x -∞, f(x) _______ ¢ As x approaches negative infinity, the function approaches _____. ¢ This tells us where the ends of the graph are going. ¢
Interval Notation The way that we write the domain, range, and intervals in increase and decrease. ¢ Brackets are used on ends that include a number and parenthesis's are used when the end number is not included. ¢ Brackets are only used in the range. ¢
Inequality Notation Another way to write the domain, range, and intervals in increase and decrease. ¢ It means the same as the interval notation. ¢