Question

Graph the parabola.

y=3x²-4
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function
button.

Answer 1

A parabola is a curve with a focus and a directrix. The focus is any point is at an equal distance while the directrix is a fixed line. The vertex of the parabola is (2,1), the two points to the right are (3,4) & (4,13) while the two points to the left are (1,4) & (0,13).

Given that:

y = 3(x - 2)² +1

A parabola is represented as:

y = a (x − h)² + k

Where:

Vertex = (h, k)

So, by comparison; the vertex of the function is:

Vertex = (2, 1)

To plot two points to the right, we select x values greater than 2.

Let: x = 3

So, we have:

y = 3(x - 2)² + 1

y = 3(3 − 2)² + 1

y = 4

Let x = 4

y = 3(x - 2)² + 1

2:37

4G 15%

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Mathematics

5 points

Let x = 4

y = 3(x - 2)² +1

y = 3(4-2)² + 1

y = 13

To plot two points to the left, we select x values less than 2.

Let: x = 1

So, we have:

y = 3(x - 2)² +1

y = 3(1 − 2)² + 1

y = 4

Let x = 0

= 3(x - 2)² + 1 y =

y = 3(02)² +1

= 13

In conclusion:

• The vertex of the parabola is (2,1)

• The two points on the right are (3,4) and (4,13)

• The two points on the left are (1,4) and (0,13)