Algebra

Hello. I am trying to solve quadratic functions but I'm having difficulty understanding. Here is my work so far...

y=3x^2 + 12x + 9
12/6 = -2 = y
3(-2)^2 + 12(-2) + 9 = -3
x=0 y=9 (0,9)

Would I just plug in 1 and 2 for x and then reflect it while i'm graphing?

So, if I do that, should it come out...

x=1
-----
y=3(1)^2 + 12(1) + 9
y=3+12+9
y=24 (1,24)

x=2
------
y=3(2)^2 + 12(2) + 9
y=12+24+9
y=45 (2,45)

Would this be correct?

  1. 👍 0
  2. 👎 0
  3. 👁 210
  1. you are correct on the points 1,24 and 2,45

    The first part, I do not understand what you were doing.

    1. 👍 0
    2. 👎 0
    👨‍🏫
    bobpursley
  2. y=3x^2 + 12x + 9

    you are correct that when x = 0, y = 9 so (0,9) is on it

    However I do not know what else you are doing.
    I generally complete the square to find the axis of symmetry
    3x^2 + 12x + 9 = y
    get one by x^2 so divide by 3
    x^2 + 4 x + 3 = y/3
    subtract 3 from both sides
    x^2+4x = y/3 - 9/3 =
    add (half of 4)^2 to both sides
    x^2 + 4 x + 4 = y/3 -9/3 + 12/3
    (x+2)^2 = (1/3)(y+3)
    vertex at (-2, -3)
    vertical axis of symmetry at x = -2

    1. 👍 0
    2. 👎 0
  3. Well, I'm trying to find two different points by changing the x value since I need to graph these points and then reflect it. I hope this helps you a little.

    1. 👍 0
    2. 👎 0
  4. ok, well reflect it about the line x = -2
    and the bottom is at (-2,-3)
    Your (1,24) and your (2,45) are fine
    so
    first point is the bottom (-2,-3)
    next is your (1,24)
    the reflection of that about x = -2 is
    3 to the left of -2 which is (-5,24)

    next do your (2,45)
    that is four to the right of the line of symmetry so go four to the left of -2 to -6
    so (-6,45)

    1. 👍 0
    2. 👎 0
  5. this might help:
    http://www.purplemath.com/modules/sqrvertx.htm

    1. 👍 0
    2. 👎 0
  6. and this:
    http://uncw.edu/courses/mat111hb/pandr/quadratic/quadratic.html

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Lesson 10: Quadratic Functions and Equations Unit Test answers please! I need the right ones

  2. Calculus

    Find expressions for the quadratic functions whose graphs are shown. One graph has the point (4,2) plotted in which the parabola passes through (U-shaped parabola- right side up) The vertex is at (3,0) and the parabola does not

  3. Algebra

    1.Solve the system of equations. y = 2x^2 - 3 y = 3x - 1 a. no solution b. (-1/2, 5), (2, -5/2) c. (-1/2, -5/2), (2,5) d. (1/2, 5/2), (2, 5) 2.how many real number solutions does the equation have 0 = -3x^2 + x - 4 a. 0 b. 1 c. 2

  4. Pre-calc/Trig...

    which of the following are quadratic functions? check all that apply 1. y=2x^2-3x+7 2. y=3x-4 3. y=(5x-3x^2)/4+1 4. y=x-x^3

  1. calculus

    Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions: If the inverses of two functions are both functions, will the

  2. Pre-Calculus

    Composition of Functions If f(x) = 2x+1 find A. f o f(x) f(f(x)) = f(2x+1) f(2x+1) = 2(2x+1) f(f(x)) = 4x +2 B. f o f o f o f(x) ^ I don't get how to solve this one C. f o f o f o f o f ...o f(x) n functions of f ^ I also don't

  3. PreCalc

    Choose any two specific functions that have inverses. Use your chosen functions to answer any one of the following questions - If the inverses of two functions are both functions, will the inverse of the sum or difference of the

  4. Math

    Lesson 8: Systems of Linear and Quadratic Equations Check my work 1. Solve the system of equations. y = 2x^2 - 3 y = 3x - 1 a. no solution b. (-1/2, 5), (2, -5/2) c. (-1/2, -5/2), (2,5)*** d. (1/2, 5/2), (2, 5) 2.how many real

  1. algebra

    Unit 4: Quadratic Functions and Equations Lesson 6: The Quadratic Formula and the Discriminant 1.) a=5, b=9, c=-4 2.) C 3.) No solution 4.) x=-2, x=1.25 5.) x=-9, x=3 6.) quadratic formula 7.) 2 8.) 11cm by 16cm

  2. algebra

    Solve this quadratic equation using the quadratic formula. x^2 + 8x - 5 = 0

  3. Pre-Calc/Trig...

    Which of the following quadratic functions has a graph that opens downwards? check all that apply A. y=2x^2-9x+3 B. y=x^2+4x+8 C. y=-(5+2x^2) D. y=60x-15x^2

  4. math

    Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions: If the inverses of two functions are both functions, will the

You can view more similar questions or ask a new question.