5.1 – Introduction to
Objectives: Define, identify, and graph quadratic
Multiply linear binomials to produce a
Standard: 2.8.11.E. Use equations to represent curves.
I. Quadratic function is any function that
can be written in the form f(x)= ax2 + bx + c,
where a ≠ 0.
Ex 2. Let f(x) = (2x – 5)(x - 2). Show that f
represents a quadratic function. Identify
a, b, and c when the function is written
in the form f(x) = ax2 + bx + c.
FOIL First – Outer – Inner – Last
(2x – 5)(x – 2) = 2x2 – 4x – 5x + 10
2x2 – 9x + 10
a = 2, b = -9, c = 10
II. The graph of a quadratic function is called a
Each parabola has an axis of symmetry, a line that
divides the parabola into two parts that are mirror
images of each other.
The vertex of a parabola is either the lowest point on
the graph or the highest point on the graph.
Ex 2. Identify whether f(x) = -2x2 - 4x + 1 has a
maximum value or a minimum value at the vertex.
Then give the approximate coordinates of the
First, graph the function:
Next, find the maximum value of the parabola (2nd,
III. Minimum and Maximum
Let f(x) = ax2 + bx + c, where a ≠ 0.
The graph of f is a parabola.
If a > 0, the parabola opens up and
the vertex is the lowest point. The y-
coordinate of the vertex is the
minimum value of f.
If a < 0, the parabola opens down
and the vertex is the highest point.
The y-coordinate of the vertex is the
maximum value of f.
Ex 1. State whether the parabola opens up or down
and whether the y-coordinate of the vertex is the
minimum value or the maximum value of the
function. Then check by graphing it in your Y =
button on your calculator. Remember: F(X) means
the same thing as Y!
a. f(x) = x2 + x – 6 Opens up, has minimum value
b. g(x) = 5 + 4x – x2 Opens down, has maximum value
c. f(x) = 2x2 - 5x + 2 Opens up, has minimum value
d. g(x) = 7 - 6x - 2x2 Opens down, has maximum value
Homework: page 278 # 14-40 even