AIgo NotesFlashcards for:
How to Graph Quadratic Functions in Intercept Form
What is the importance of the intercept form of a quadratic function?
Press to flip
The intercept form makes it easy to identify the X intercepts and understand the symmetry of the parabola.
What is the standard equation of a quadratic function in intercept form?
Press to flip
Y = a * x^2 - P * x - Q
What do P and Q represent in the intercept form of a quadratic function?
Press to flip
P and Q represent the X intercepts.
What are the X intercepts of the example quadratic function Y = a * x^2 - P * x - Q?
Press to flip
The X intercepts are (1, 0) and (3, 0).
How do you find the vertex of a quadratic function in intercept form?
Press to flip
The x-coordinate of the vertex (H) is the average of P and Q, and the y-coordinate of the vertex (K) is found by plugging H back into the original equation.
How do you determine whether a quadratic function opens upward or downward?
Press to flip
If 'a' is positive, the graph opens upward; if 'a' is negative, the graph opens downward.
What is the minimum value of a quadratic function that opens upward?
Press to flip
The minimum value is the y-coordinate of the vertex.
What is the axis of symmetry for a quadratic function?
Press to flip
The axis of symmetry is a vertical line that passes through the vertex, represented by the equation x = H.
How do you graph a quadratic function in intercept form?
Press to flip
Plot the X intercepts, find the vertex, and plot additional points symmetrically around the vertex to draw the parabola.
What are the X intercepts of the quadratic function y = 2 * x^2 - x + 3?
Press to flip
The X intercepts are (1, 0) and (-3, 0).
What is the vertex of the quadratic function y = 2 * x^2 - x + 3?
Press to flip
The vertex is at (-1, 8).
What is the maximum value of a quadratic function that opens downward?
Press to flip
The maximum value is the y-coordinate of the vertex.
What is the axis of symmetry for the quadratic function y = 2 * x^2 - x + 3?
Press to flip
The axis of symmetry is x = -1.
Why do the Y values of points equidistant from the vertex on a quadratic function have the same value?
Press to flip
This is due to the symmetry of the parabola.
How many points are typically needed to graph a quadratic function accurately?
Press to flip
At least five points, including the vertex, are needed to graph a quadratic function accurately.
What is the significance of the vertex in a quadratic function?
Press to flip
The vertex represents the minimum or maximum value of the function and is the axis of symmetry.
How can you find the Y intercept of a quadratic function?
Press to flip
The Y intercept is found by setting x = 0 in the equation and solving for y.
What is the difference between a minimum and a maximum value in a quadratic function?
Press to flip
A minimum value occurs in a parabola that opens upward, while a maximum value occurs in a parabola that opens downward.
How does the sign of 'a' in the quadratic equation affect the shape of the graph?
Press to flip
The sign of 'a' determines whether the parabola opens upward (positive 'a') or downward (negative 'a').
What is the importance of the intercept form of a quadratic function?
Press to flip
The intercept form makes it easy to identify the X intercepts and understand the symmetry of the parabola.
What is the standard equation of a quadratic function in intercept form?
Press to flip
Y = a * x^2 - P * x - Q