Anonymous

# For the equation y = 6+6x-(1/3)x^2?

For the equation y = 6+6x-1/3x^2

graph the equation using the vertex and at least four other points.

I missed this when my teacher taught it. I don't know how it would look on a graph.

However, I think the vertex is f(6)=6+54-27=33

So, please if you have the time show me the graph pf the equation using the vertex and at least four other points.

Thank you very very very very much.

Relevance

The vertex is f(9) = 33.

To make the graph, just choose some x values around the vertex (see more info in http://en.wikipedia.org/wiki/Quadratic_equation )

for example:

....x ...........y

-20 -247.33

-10 -87.33

0 6

9 33

20 -7.33

40 -287.33

I can't paste the figure here with the graph, but it looks like a hill, with the maximum at x = 9

• Login to reply the answers
• You're really careless with signs, I'm saying this firsthand. Assuming the (-) in the beginning of each line is not intended to be a minus symbol. (be careful with that, never use this symbol to mark headlines in math; in fact, don't mark anything at all) (y) for correct and (n) for incorrect I'm gonna save space from the variables, so interpret (1, 2, 3) as x^2 + 2x + 3, etc 1. (3, 4, 1) + (4, 5, -1) = (3 + 4), (4 + 5), (1 - 1) = 7, 9, 0 (n) 2. (6, 5, 3) + (4, 2, -7) = (6 + 4), (5 + 2), (3 - 7) = 10, 7, -4 (n) 3. (6, 11, -7) - (5, 3, -10) = (6, 11, -7) + (-5, -3, 10) = (6 - 5), (11 - 3), (-7 + 10) = 1, 8, -3 (n) 4. (12, 3, 7) - (7, 1, 9) = (12 - 7), (3 - 1), (7 - 9) = 5, 2, -2 (n) You need to know that x^m * x^m = x^(m + n) not x^(m*n) 5. (4x^3)(x^4) = 4(x^3*x^4) = 4*x^(3 + 4) = 4x^7 (n) When multiplying 2 sums, you have to multiply out all the possible pairs, not just the first and last. (a + b)(c + d) = ac + bc + ac + ad 6. (3x + 1)(x - 2) = 3x*x + x - 3x*2 - 1*2 = 3x^2 + x - 6x - 2 = 3x^2 - 5x - 2 (n) 7. (5x - 1)(2x - 2) = 5x*x - 1*2x - 5x*2 + -1*-2 10x^2 - 2x - 10x + 2 = 10x^2 - 12x + 2 (n) Point-slope formula: All the lines with slope m and point (x1, y1), has equation y - y1 = m(x - x1) 8. y - 4 = 3(x + 1) --> y - 4 = 3x + 3 --> y = 3x + 7 (y) 9. y + 3 = 4(x - 2) --> y + 3 = 4x - 8 --> y = 4x - 11 (n) 10. 4x + 3 > 6x - 1 --> 4x - 6x > -1 - 3 --> -2x > -4 --> x < -4/-2 --> x < 2 (n) 11. (4x^2 + 2x + 1)(x - 5) = (4x^2 + 2x + 1)*x - (4x^2 + 2x + 1)*5 = (4x^3 + 2x^2 + x) - (20x^2 + 10x + 5) = 4x^3 + 2x^2 + x - 20x^2 - 10x - 5 = 4x^3 - 18x^2 - 9x - 5 (n) 12. (7x^2 + x + 3)(x - 4) = (7x^2 + x + 3)*x - (7x^2 + x + 3)*4 = 7x^3 + x^2 + 3x - 28x^2 - 4x - 12 = 7x^3 - 27x^2 - x - 12 (y) You'll want to know that (a + b)^2 does not equal a^2 + b^2 (try it out with any integers) 13. (4x + 3)^2 = (4x + 3)(4x + 3) = 16x^2 + 12x + 12x + 9 = 16x^2 + 24x + 9 (n) For quicker calculation use this formula for square of a sum (a + b)^2 = a^2 + 2ab + b^2 You got a total of 2/13. That's not good at all :(

• Login to reply the answers
• to graph four points,just plug in 4 values for x and see what you get for y each time. those will be your coordinates for four points. the graph should be a parabola. try some x values on both sides of the x-axis.im not sure about your vertex. i thinks its (9,33)

• Login to reply the answers
• y = 6+6x-1/3x^2

3y=18 +18 x - x^2; multiply 3 to make it whole number

3y -99= -x^2 +18x -81 to make the equation a perfect square

-3(y+33)=[x-9]^2

the opening was downward

V=(9,-33)

: j

• Login to reply the answers