WRITE EQUATIONS OF PARABOLAS IN VERTEX FORM FROM GRAPHS

Write the equation of the parabola in vertex form.

Problem 1 :

Solution :

The parabola opens up. The minimum point is at (0, -5).

Vertex (h, k) ==> (0, -5)

Equation of parabola :

y = a(x - h)² + k

y = a(x - 0)² + (-5) ----(1)

By observing the graph, the parabola passes through the point (2, -1).

-1 = a(2 - 0)² + (-5)

-1 = 4a + (-5)

-1 + 5 = 4a

4a = 4

a = 4/4

a = 1

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

y = 1(x - 0)² + (-5)

y = x² - 5

Problem 2 :

Solution :

The parabola opens up. The minimum point is at (0, 2).

Vertex (h, k) ==> (0, 2)

Equation of parabola :

y = a(x - h)² + k

y = a(x - 0)² + 2 ----(1)

By observing the graph, the parabola passes through the point (1,3).

3 = a(1 - 0)² + 2

3 = a + 2

a = 3 - 2

a = 1

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

y = 1(x - 0)² + 2

y = x² + 2

Problem 3 :

Solution :

The parabola opens up. The minimum point is at (2, 0).

Vertex (h, k) ==> (2, 0)

Equation of parabola :

y = a(x - h)² + k

y = a(x - 2)² + 0 ----(1)

By observing the graph, the parabola passes through the point (3, 1).

1 = a(3 - 2)²

1 = a(1)

a = 1

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

y = 1(x - 2)²

y = (x - 2)²

Problem 4 :

Solution :

The parabola opens up. The maximum point is at (0, 4).

Vertex (h, k) ==> (0, 4)

Equation of parabola :

y = a(x - h)² + k

y = a(x - 0)² + 4 ----(1)

By observing the graph, the parabola passes through the point (1, 2).

2 = a(2 - 0)² + 4

2 = a(4) + 4

4a = 2 - 4

4a = -2

a = -2/4

a = -1/2

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

y = (-1/2)(x - 0)² + 4

y = (-1/2)x² + 4

Problem 5 :

Solution :

The parabola opens up. The maximum point is at (-3, 5).

Vertex (h, k) ==> (-3, 5)

Equation of parabola :

y = a(x - h)² + k

y = a(x - (-3))² + 5

y = a(x + 3)² + 5----(1)

By observing the graph, the parabola passes through the point (-4, 2).

2 = a(-4 + 3)² + 5

2 = a(1)² + 5

a = 2 - 5

a = -3

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

y = -3(x + 3)² + 5