Algebra

The vertex of a parabola represented by f(x)=x^2-4x+3 has coordinates of (2,-1). Find the coordinates of the vertex of the parabola defined by g(x)=f(x-2). Explain how you arrived to your answer.
My question: Would you move the parabola represented by f(x) 2 spaces to the right to get the parabola represented by g(x)?

  1. 👍 0
  2. 👎 0
  3. 👁 873
  1. yes,
    the new vertex will be (4,-1)

    proof:
    f(x-2) = (x-2)^2 - 4(x-2) + 3
    = x^2 - 4x + 4 - 4x + 8 + 3
    = x^2 - 8x + 15
    = g(x)
    vertex of g(x) = -b/(2a)
    = 8/2 = 4
    g(4) = 4^2 - 8(4) + 15 = -1
    vertex is (4,-1)

    1. 👍 2
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    M is the midpoint of line AN, A has coordinates (-6,-6) and M has coordinates (1,2). Find the coordinates of N.

  2. math

    Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

  3. math

    Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.

  4. geometry

    B is the midpoint of AC. A has coordinates (-3,4), and B has coordinates (-1 1/2,1). Find the coordinates of C. Did i get the right answer? (2)-1 1/2=(2)-3+x(over 2) -3-3=3+x-3 -6=x (2)1=(2)4+y(over 2) 2-4=4+y-4 -2=y The

  1. Mathematics

    Right △ABC has coordinates A(-7, 3), B(-7, 10), and C(-1, 3). The triangle is reflected over the x-axis and then reflected again over the y-axis to create △A'B'C'. Which are the coordinates of vertex A'?

  2. Math

    a. Express f(x)=x^2 - 6x + 14 in the form f(x)=(x-h)^2 + k, where h and k are to be determined. b.Hence, or otherwise, write down the coordinates of the vertex of the parabola equation y=x^2 - 6x + 14.

  3. geometry

    Three vertices of a parallelogram WXYZ are X(-2, -3) Y(0, 5) and Z(7, 7). Find the coordinates of vertex W. a (4, 0) b (5, 0) c (9, 15) d (5, -1)

  4. geometry

    Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line.

  1. Math

    A person standing close to the edge on the top of a 160-foot building throws a baseball vertically upward. The quadratic function s(t) = -16t^2 +64t + 160 models the ball's height above the ground, s(t), in feet, t seconds after

  2. Algebra 2

    What is the y-intercept, the equation of the axis of symmetry, and the x-coordinates of the vertex? Can you also make table of values that includes the vertex? f(x) = 3x^2 + 8x

  3. math

    points P(4,12), Q(9,14), and R(13,4)are the three vertices of a rectangle. a. find the coordinates of the fourth vertex, S. b. write a short description of how you found the coordinates of S. c. find the lengths of the diagonals

  4. Pre-calculus HELP PLEASE !

    Find the coordinates of the center of the ellipse represented by 4x^2 + 9y^2 – 18y – 27 = 0. For 2x^2 + xy + 2y^2 = 1, find , the angle of rotation about the origin, to the nearest degree. Find the distance between points at

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