How to make a Quadratic Function Graph

The Quadratic Function formula

The formula or the general form of quadratic function is:

f(x) = ax² + bx + c

Information :
a, b, and c ∈ R
a ≠ 0
Quadratic function graph is parabolic with the equation y = ax² + bx + c.

How to make a Quadratic Function Graph

Here are 5 steps for making a graph of quadratic functions, such as:

The cutting point of the graph with the x-axis, by taking y = 0
The cutting point of the graph with the y-axis, by taking x = 0
The symmetry axis of the graph is x = -b/2a
The return or vertex coordinates (x, y), where x = -b/2a and y = -D/4a with D = b² - 4ac
Graph open down if a < 0 and open up if a > 0.

Example:
Draw a graph of f(x) = x² - 2x - 8 with the domain of real numbers!

Answer:
Is known :
f(x) = x² - 2x - 8
y = x² - 2x - 8

a = 1
b = -2
c = -8

1. The cutting point of the graph with the x-axis, by taking y = 0
y = x² - 2x - 8
0 = x² - 2x - 8
0 = (x - 4)(x + 2)
x - 4 = 0 or x + 2 = 0
x = 4 or x = -2

Then the intersection with the x axis is (-2, 0) and (4, 0).

2. The cutting point of the graph with the y-axis, by taking x = 0
y = x² - 2x - 8
y = 0² - 2(0) - 8
y = -8

Then the intersection of the graph with the y-axis is (0, -8).

3. The symmetry axis of the graph is x = -b/2a
x = -b/2a
x = -(-2)/2(1)
x = 2/2
x = 1

So the symmetry axis is 1

4. The return or vertex coordinates (x, y), where x = -b/2a and y = -D/4a with D = b² - 4ac
x = -b/2a
x = -(-2)/2(1)
x = 2/2
x = 1

y = -D/4a
y = -(b² - 4ac)/4a
y = -(-2² - 4(1)(-8))/4(1)
y = -(4 + 32)/4
y = -36/4
y = -9

The coordinates of the turning point are (1, -9).

5. Graph open down if a < 0 and open up if a > 0
Because a > 0, so the graph opens up. Below is the graph: