What is y=x^2+74, translated 2 units up and 5 units left

y = x² + 10x + 101

Step-by-step explanation:

Start with the basic function: y = x² + 74.

To shift the parabola up two units, you add two units to the value of y. The equation becomes

y = x² + 76

To shift the parabola five units to the left, you must add five units to the value of x. The equation for the parabola becomes

y = (x + 5)² + 76

y = x² + 10x + 25 + 76

y = x² + 10x + 101

The figure below shows the graphs of

y = x² (red)

y = x² + 76 (blue) (shifted up two units)

y = x² + 10x + 101 (green) (shifted left five units)

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.