math

HELP Not great in these
Express y=2x^2 -12x +23 in the form
y=2(x-c)^2 + d

The graph of y=x^2 is transformed into the graph of y=2x^2 - 12x +23 by the transformation

a vertical stretch with scale factor k followed by,
A horizontal translation of p units followed by,
a vertical translation of q units

what are the values of k, p , and q

HELP PLEASE!

  1. 👍 1
  2. 👎 0
  3. 👁 780
asked by Morie
  1. 2x^2 -12x +23=2*(x^2-6x+23/2)

    (x-a)^2= x^2-2ax+a^2

    (x-3)^2= x^2-2*3*x+3^2= x^2-6x+3^2

    2*(x^2-6x+23/2)=
    =2*(x^2-2*3*x +3^2+ 23/2 -3^2)
    =2(x^2-6x+3^2)+2*(23/2)-2*(3^2)
    =2*(x-3)^2+23-2*9
    =2*(x-3)^2+23-18
    =2*(x-3)^2 +5

    Proof:

    2*(x-3)^2+5=2*(x^2-2*3*x+3^2)+5
    =2*(x^2-6x+9)+5
    =2x^2-12x+18+5=2x^2-12x+23

    So:
    2x^2 -12x +23 = 2*(x-3)^2 +5

    a vertical stretch =2

    a y-intercept is a point where the graph of a function intersects with the y-axis

    2*0^2-12*0+23=0-0+23=23

    vertical translation = 23

    Quadratic function have extreme point
    for x=-(b/2a)
    In this case a=2 b=-12
    -(b/2a)=-[(-12/(2*2]=-(-12/4)=12/4=3


    2x^2 -12x +23 = 2*(x-3)^2 +5

    k=2

    p=3

    q=23

    1. 👍 0
    2. 👎 0
    posted by Bosnian

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra. Please check my answers

    Evaluate a/b+c^d for a=6,b=3,c=4 and d=5 A.42*** B.18 C.82 D.360 What is the simplified form of the expression ? -(12x-8y) A.12x+8y B.12x-8y***** C.-12x+8y D.-12x-8y

    asked by Help please on September 3, 2015
  2. Algebra 1

    1) what is the simplified form of (x-2)(2x+3)? Use the distributive property. A) 2x^2-x-6 B) 2x^2-6 C)2x^2-7x-6 D) 2x^2 +x-6**** 2) what is the simplified form of (3x+2)(4x-3) use a table. A)12x^2+18x+6 B) 12x^2+x-6 C)

    asked by Tris on February 9, 2015
  3. MATH D:

    Evaluate "12x" when x=5/6. Express in simplest form.

    asked by Hey[: on January 9, 2012
  4. Pre-Calculus

    Find all solutions of the equation and express them in the form a + bi. 36x^2 − 12x + 2 = 0

    asked by Christian on September 14, 2014
  5. Calculus

    Express the quadratic function y=-2/3x2-12x-11 in standard form?

    asked by Josh on July 11, 2011
  6. Algebra

    What is the vertex form of the equation? y = -x^2+12x-4 My work: -(x^2 + 12x)-4 -(x^2 + 12x + 36)-4 + 36 Y= -(x+36)^2 + 32 Is this correct? I am not sure if I did this right or not? Thank you!

    asked by Mitch n' Joey on October 25, 2017
  7. Math

    Which expression is the expanded form of p(x)=4(x−7)(2x2+3)? 8x3−56x2+12x−84 8x3+56x2−12x−84 32x3−224x2+48x−336 −48x2+12x−84 I believe it is 8x3−56x2+12x−84 if I am wrong can you explain

    asked by BS on December 6, 2019
  8. math

    write this equation in standard form. y=1/2x2+12x-8 y equals one half x squared plus 12x minus 8

    asked by matt on February 2, 2010
  9. Pre-Cal

    I'm trying to put this parabola in standard form which is: (y-k)^2=4p(x-h) The equation is x=(1/12)(y-2)^2 +6 Here is what i have so far: x=(1/12)(y-2)^2 +6 -6 -6 x-6=(1/12)(y-2)^2 *12 *12 Would it be 12x-6 OR 12x-72? thanks

    asked by Lala on April 3, 2012
  10. math

    Can someone please check ny answers and tell me if I'm correct? I did the FOIL method for each of these.. 1.What is the simplified form of (x-2)(2x+3) My answer; 2x^2-x-6 2.What is the simplified form of (3x+2)(4x-3)? My answer;

    asked by Sage on February 29, 2016

More Similar Questions