Advanced functions

Given the formula: f(x)=x^2+ax+b and the vertex point (3,9)
prove that this is the vertex of a minimum parabola using instantaneous rate of change.

  1. 👍 0
  2. 👎 0
  3. 👁 144
  1. y = x^2 + ax + b
    dy/dx = 2x + a
    = 0 at the vertex
    so x = -a/2
    but the vertex is (3,9)
    so 3 = -a/2
    a = -6
    also (3,9) satisfies y = x^2 + ax + b, and we know a = -6
    9 = 9 - 6(3) + b
    b = 18

    check:
    y = x^2 - 6x + 18
    completing the square:
    y = x^2 - 6x + 9 - 9 + 18
    = (x-3)^2 + 9 , whose vertex is (3,9)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. geometry

    Trisha drew a pair of line segments starting from a vertex. Which of these statements best compares the pair of line segments with the vertex? Answer A:Line segments have two endpoints and a vertex is a common endpoint where two

  2. Help please with reflection problem!?

    A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of

  3. Math

    Write the formula for absolute value function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).

  4. geometry

    Which of the following is the fourth step in copying an angle? A) place the compass on the vertex of the new angle and swing an arc similar to the first one you created. b) open the compass to the width of the intersection points

  1. Pre Cal

    write the equations of the parabola, the directrix, and the axis of symmetry. vertex: (-4,2) focus: (-4,6) if someone could explain how to do this problem then that would be great! thanks in advance! Formats to help you find the

  2. math

    Two vertices of a triangle lie on some line. The third vertex belongs to the line that is parallel to the first one. Prove the area of that triangle does not depend on the position of the third vertex on the line.

  3. math

    A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola.

  4. Maths

    abcd is a parallelogram.if the line joining the mid-point of side bc to vertex a bisects angle a,then prove that bisector of angle b also bisects ad​ Hint Consider BG as the angle bisector of B that meets AD at G. Now, you have

  1. Math

    Write a formula for quadratic function if its graph has the vertex at point (−2,5) and passes through the point (3,−10).

  2. Algebra 2

    3. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2 – 3. (1 point) A- vertex: (2, –3); axis of symmetry: x = 2 B- vertex: (–2, –3); axis of symmetry: x = –2 C- vertex: (2, 3); axis

  3. algebra

    Identify the vertex and axis of symetry of the parabola. Identify points corresponding to P and Q. on the graph it has P at (-2,4) and a point at Q at (-1,7). my teacher says the answers were the vertex was (-1,3) the Axis of

  4. Algebra

    Identify the vertex and the axis of symmetry for the graph of y=5(x-2)^2 + 3. a) vertex (2,3); x = -2 b) vertex (-2,-3); x = 2 c) vertex (2,3); x = 2 d) vertex (-2,-3); x = -2 I have no idea how to solve this problem! Please help.

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