WRITING QUADRATIC EQUATIONS IN VERTEX FORM USING A GRAPH

Determine the equation of quadratic function from graph. Give the function in vertex form.

Example 1 :

Solution :

The vertex is at (0, 1).

y = a(x - h)² + k

y = a(x - 0)² + 1----(1)

The parabola is passing through the point (1, 2).

2 = a(1 - 0)² + 1

2 - 1 = a(1 - 0)²

1 = a(1)

a = 1

By applying the value of a in (1), we get

y = 1(x - 0)² + 1

y = x² + 1

So, the equation of the parabola is y = x² + 1.

The coefficient of x² is 1, we see the evidence that the parabola opens up.

Example 2 :

Solution :

The vertex is at (-3, -1).

y = a(x - h)² + k

y = a(x + 3)² - 1 ---(1)

The parabola is passing through the point (-2, -2).

-2 = a(-2 + 3)² - 1

-2 + 1 = a(1)²

1 = a

By applying the value of a in (1), we get

y = 1(x + 3)² - 1

So, the equation of the parabola is y = (x + 3)² - 1.

Example 3 :

Solution :

The vertex is at (0, -2).

y = a(x - h)² + k

y = a(x + 0)² - 2 ---(1)

The parabola is passing through the point (-2, 2).

2 = a(-2 + 0)² - 2 

2 + 2 = a(-2)²

4 = 4a

a = 1

By applying the value of a in (1), we get

y = 1x² - 2

So, the equation of the parabola is y = x² - 2

Example 4 :

Solution :

The vertex is at (1, 1).

y = a(x - h)² + k

y = a(x - 1)² + 1 ---(1)

The parabola is passing through the point (0, 2).

2 = a(0 - 1)² + 1

2 - 1 = a(-1)² 

1 = a

By applying the value of a in (1), we get

y = 1(x - 1)² + 1

So, the equation of the parabola is y = 1(x - 1)² + 1.