What is the equation of the quadratic graph with a focus of (3, -1) and a directrix of y = 1?

The equation of the quadratic graph is y =   (x - 3)²

Step-by-step explanation:

The standard form of the equation of the quadratic graph is

(x - h)² = 4p(y - k), where

∵ The focus is (3, -1)

∵ The focus is (h, k + p)

→ Compare them

∴ h = 3

∴ k + p = -1 ⇒ (1)

∵ The directrix is at y = 1

∵ The directrix is at y = k - p

→ Compare them

∴ k - p = 1 ⇒ (2)

→ Add equations (1) and (2) to eliminate p

∵ (k + k) + (p - p) = (-1 + 1)

∴ 2k + 0 = 0

∴ 2k = 0

→ Divide both sides by 2

∴ K = 0

→ Substitute the value of k in equation (1) to find p

∵ 0 + p = -1

∴ p = -1

→ Substitute the values of h, k, and p in the form of the equation above

∵ (x - 3)² = 4(-1)(y - 0)

∴ (x - 3)² = -4(y)

∴ (x - 3)² = -4y

→ Divide both sides by -4

∴ (x - 3)² = y

→ Switch the two sides

∴ y =   (x - 3)²

∴ The equation of the quadratic graph is y =   (x - 3)²

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: