Graphing Parabolas Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Identify the key features of

f(x) = x^2 - 4x + 3

for graphing.

Solution

1
Direction: $a = 1 > 0$ , opens upward.
2
Vertex: $x = -\frac{-4}{2} = 2$ ; $f(2) = 4 - 8 + 3 = -1$ . Vertex: $(2, -1)$ .
3
$y$ -intercept: $f(0) = 3$ , point $(0, 3)$ .
4
$x$ -intercepts: factor $x^2 - 4x + 3 = (x-1)(x-3) = 0$ , so $x = 1$ and $x = 3$ .

Answer

Vertex

(2,-1)

, opens up,

x

-intercepts at 1 and 3,

y

-intercept at 3.

To graph a parabola, find: (1) direction from the sign of

a

, (2) vertex, (3)

y

-intercept at

x=0

, (4)

x

-intercepts by setting

f(x) = 0

About Graphing Parabolas

The process of plotting a quadratic function by identifying its key features: vertex, axis of symmetry, direction of opening, $y$ -intercept, and $x$ -intercepts (if they exist).

Learn more about Graphing Parabolas →

More Graphing Parabolas Examples

Example 2 medium

Sketch [formula]. Find vertex and intercepts.

Example 3 easy

Does [formula] have any [formula]-intercepts?

Example 4 medium

The vertex of a parabola is [formula] and it passes through [formula]. Find the equation.

← All Graphing Parabolas Examples Graphing Parabolas Concept

Related Concepts

Quadratic Vertex Form Coordinate Plane Vertex and Axis of Symmetry Function Transformation