how do you graph y = square root (3 - x)?

without a data, tables of values or even calculator.

1)

y = 2√(9-x^2)

Parent function:

y = 2√(9-x^2)

y^2 = 4 * (9-x^2)

y^2 = 36 - 4x^2

4x^2 + y^2 = 36

x^2/9 + y^2/36 = 1 <==== ellipse.

since we are taking the POSITIVE root, y = 2√(9-x^2), the graph will be along the +y = axis. which we can say above the x-axis.

its center at (0,0).

the maximum point on the +y-axis, is √(36) = 6

the half circle extends along the +x-axis & -x-axis as √(9) = +/- 3

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2)

y = -3√(4 - (x + 1)^2 )

Parent function:

y^2 = 9 * (4 - (x + 1)^2 )

y^2 = 36 - 9 (x + 1)^2

9 (x + 1)^2 + y^2 = 36

(x + 1)^2/4 + y^2/36 = 1 <==== ellipse

its center at (-1 , 0)

since we are taking the NEGATIVE root, it will be below the x-axis which is along the -y-axis.

the minimum point that goes along the -y-axis is √(36) = +/-6 ( i need -6 )

along the x-axis:

it will be as √(4) = +/- 2 ......but since i have (x + 1)^2, it will shift to the left on more unit.

so the units along the x-axis are -3 & 1

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free to e-mail if have a question.

first re -write the equation in this form; x + 2y=-4 - (a million) -3x+4y=12 - (2) multiply (a million) by using -3 and (2) by using a million -3x+6y=12 - (3) -3x+4y=12 - (4) subtract (4) from (3) 2y =0 y=0/2 =0 then replace y in (a million) x+2(2) = -4 x +4 =-4 x =-4-4 = -8 (x = -8, y = 0)