Solving Quadratic Equations and their Graphs

Steps in how to solve quadratic equations and getting their graphs

Graph of f(x) = x² + k

Example 1: g(x) = x² + 3

Step 1:

To graph the example, we'll need a given table of values, so we will make one.

g(x) 

-3/

-2/

-1/

0/

1/

2/

3/

Step 2:

Then after, we will replace x with the given numbers and solve.

g(-3) = (-3)² + 3

g(-3) = 9 + 3

g(-3) = 12

g(-2) = (-2)² + 3

g(-2) = 4 + 3

g(-2) = 7

g(-1) = (-1)² + 3

g(-1) = 1 + 3

g(-1) = 4

g(0) = (0)² + 3

g(0) = 3

g(1) = (1)² + 3

g(1) = 1 + 3

g(1) = 4

g(2) = (2)² + 3

g(2) = 4 + 3

g(2) = 7

g(3) = (3)² + 3

g(3) = 9 + 3

g(3) = 12

g(x)  x  

-3/12

-2/7

-1/4

0/3

1/4

2/7

3/12

Step 3:

Then, after solving and finishing the table of values, we will graph.

Graph of g(x) = x²

Example 2: g(x) = x²

Step 1:

To graph g(x) = x², you will need a table of values, so let's make one.

g(x) x

-3/

-2/

-1/

0/

1/

2/

3/

Then, we'll replace x with the given and multiply/raise it to the power of 2.

g(-3) = (-3)²

(-3)² = 9

-3² = 9

g(-2) = (-2)²

(-2)² = 4

-2² = 4

g(-1) = (-1)²

(-1)² = 1

-1² = 1

g(0) = (0)²

(0)² = 0

0² = 0

g(1)² = 1

(1)² = 1

1² = 1

g(2) = (2)²

(2)² = 4

2² = 4

g(3) = (3)²

(3)² = 9

3² = 9

g(x) x

-3 / 9

-2 / 4

-1 / 1

0 / 0

1 / 1

2 / 4

3 / 9

Step 3:

Then, after multiplying and getting the g(x), we will graph the answers we got from multiplying the given.