Consider the function: f(x) = 2x^2 - 1.5x - 5 and its graph. If the graph of f(x) is:

(i) first translated 2 units in the positive x direction and 3 units in the positive y

direction

(ii) then, stretched vertically by a factor of 2

(iii) and then reflected across the x-axis

What is the resultant function in standard form and its graph?

f(x) = -4x² + 19x - 18

Step-by-step explanation:

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

f(x) = 2x² - 9.5x + 6

If it is then translated 3 units in the positive y, we add 3 to the input function to get:

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

iii) reflected across the x-axis

we multiply the parent function by –1, to get a reflection about the x-axis.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

step-by-step explanation: