Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?

f(x) = (x - 2)² + 2

Step-by-step explanation:

From any point (x, y ) on the parabola the focus and the directrix are equidistant.

Using the distance formula

= | y + 2 | ← square both sides

(x - 2)² + (y - 6)² = (y + 2)² ← subtract (y + 2)² from both sides

(x - 2)² + (y - 6)² - (y + 2)² = 0 ← subtract (x - 2)² from both sides

(y - 6)² - (y + 2)² = - (x - 2)² ← expand left side using FOIL and simplify

y² - 12y + 36 - y² - 4y - 4 = - (x - 2)²

- 16y + 32 = - (x - 2)² ← subtract 32 from both sides

- 16y = - (x - 2)² - 32 ← divide all terms by - 16

y = (x - 2)² + 2

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

need more info

step-by-step explanation: