Question

Pls help i need this fast

Answer 1

Based on the graph shown above, an equation for the quadratic function is
`g(x) = (x - 2)^2 - 1`.

In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

`y = a(x - h)^2 + k`

Where:

• h and k represents the vertex of the graph.
• a represents the leading coefficient.

Based on the information provided above, we can determine the value of a by using the vertex (2, -1) and point (4, 3) as follows:

`y = a(x - h)^2 + k\\\\3 = a(4 - 2)^2 - 1\\\\`

3 = 4a - 1

4a = 3 + 1

a = 4/4

a= 1

Therefore, the required quadratic function that represents g(x) can be written as follows;

`y = a(x - h)^2 + k\\\\g(x) = (x - 2)^2 - 1`