Question

5. Write the equation of the following araph in intercent form.

Answer 1

The quadratic equation
`y = (2)/(5)\cdot x^2 - (6)/(5)\cdot x - 4` represents the function on the graph.

How to determine the quadratic equation that represents the graph

In this problem we find the representation of a quadratic equation, whose definition is described by following equation:

y = a · x² + b · x + c

Where:

• a, b, c - Real coefficients.
• x - Independent variable.
• y - Dependent variable.

All coefficients can be found from the knowledge of three distinct points. First, determine the points set on Cartesian plane:

(x₁, y₁) = (- 2, 0), (x₂, y₂) = (0, - 4), (x₃, y₃) = (5, 0)

Second, solve the resulting system of linear equations:

4 · a - 2 · b + c = 0

c = - 4

25 · a + 5 · b + c = 0

`(a, b, c) = \left((2)/(5), -(6)/(5), - 4\right)`

Third, write the resulting quadratic equation:

`y = (2)/(5)\cdot x^2 - (6)/(5)\cdot x - 4`