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Quadratic Function:
f(x) = ax2 + bx +c where a 0.
The graph of a quadratic
function is called a parabola.
Special Parts of a Parabola:
Axis of Symmetry: A vertical line that passes through the
vertex.
http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html
Special Parts of a Parabola:
Axis of Symmetry: This line is midway between the x-intercepts
therefore it is the “average” of the x-values.
http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html
Discriminant:• If b2 – 4ac > 0
Parabola crosses x-axis twice. There will be two x-intercepts.
• If b2 – 4ac = 0Parabola is tangent to the
x-axis. There is only one x-intercept.
Discriminant:• If b2 – 4ac > 0
Parabola crosses x-axis twice. There will be two x-intercepts.
• If b2 – 4ac = 0Parabola is tangent to the
x-axis. There is only one x-intercept.
• If b2 – 4ac < 0Parabola never crosses the x-axis so there are no x-intercepts.
Find the intercepts, axis of Find the intercepts, axis of symmetry, and the vertex of symmetry, and the vertex of
the given parabola.the given parabola.
y = (x + 4)(2x – 3)y = (x + 4)(2x – 3)
Sketch the graph of the parabola. Label Sketch the graph of the parabola. Label the intercepts, the axis of symmetry, the intercepts, the axis of symmetry,
and the vertex.and the vertex.
y = 2xy = 2x22 – 8x + 5 – 8x + 5
If the equation can be written in the form of :
then the vertex of the parabola is (h, k) and the axis of symmetry is the equation
x = h.
Find the vertex of the Find the vertex of the parabola by completing the parabola by completing the
square.square.
y = -2xy = -2x22 + 12x + 4 + 12x + 4
Now, find the x- and y-Now, find the x- and y-intercepts.intercepts.
y = -2xy = -2x22 + 12x + 4 + 12x + 4
Find the equation of the quadratic Find the equation of the quadratic function function ff with with ff(-1) = -7 and a (-1) = -7 and a maximum value maximum value ff(2) = -1. Show (2) = -1. Show
that the function has no that the function has no xx-intercepts.-intercepts.
Where does the line y = 2x + 5 intersect the parabola y = 8 – x2?
*Show this both algebraically and graphically.
Find an equation of the function whose graph is a parabola with x-intercepts 1
and 4 and a y-intercept of -8.