Question

Given the following information, write an equation

that represents the quadratic function.
a) Vertical Translation down 9 units
b) Horizontal Translation right 2 units
c) Coordinate point (4,-5)

Answer 1

The vertical and horizontal translations of the quadratic function and the given coordinate point lead us to the function f(x) = (x - 2)^2 - 9.

Step-by-step explanation:

We can approach this problem step by step to create the quadratic function based on the given translations and coordinate point.

Step 1: Determine the basic form

The general form of a quadratic function is f(x) = ax^2 + bx + c. However, when we include translations, this changes to f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Step 2: Apply the translations

A vertical translation down 9 units means our k value is -9. A horizontal translation to the right 2 units means our h value is 2. Our equation so far is f(x) = a(x - 2)^2 - 9.

Step 3: Use the coordinate point

Substitute the coordinate point (4, -5) into the equation resulting in -5 = a(4 - 2)^2 - 9, which simplifies to -5 = 4a - 9. Solving for a gives us a = 1. Hence, the equation of our quadratic function is f(x) = (x - 2)^2 - 9.