Integrated Math 1

posted by .

Suppose a parabola f(x) has its vertex at (0, 25) and its zeros at x = -5 and x = 5. Then f(x)equals _____.

A. 25-x^2

B. 1- 1/25 x^2

C. x^2-1

D. x^2-25

  • Integrated Math 1 -

    The standard equation of a parabola is :

    y = a x ^ 2 + bx + c


    The vertex of a parabola is the point where the parabola crosses its axis.

    If the coefficient of the x ^ 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “U”-shape.

    If the coefficient of the x ^ 2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “U”-shape

    But the equation for a parabola can also be written in "vertex form":

    y = a * ( x – h ) ^ 2 + k

    Where point (h, k) is the vertex.

    You can see how this relates to the standard equation by multiplying it out:

    y = a ( x – h ) * ( x – h ) + k

    y = a * ( x ^ 2 - 2 * x * h + h ^ 2 ) + k

    y = a x ^ 2 – 2 * a * h * x + a * h ^ 2 + k

    The coefficient of x here is –2 a h.

    This means that in the standard form ;

    y = a * x ^ 2 + b * x + c

    the expression

    - b / 2 a

    gives the x - coordinate of the vertex.

    In this case - b / 2 a = 0

    that means b = 0 so equation of a parabola is :

    y = a x ^ 2 + c


    for x = 0 y = 25

    25 = a * 0 ^ 2 + c

    25 = c

    c = 25

    for x = - 5 y = 0

    0 = a * ( - 5 ) ^ 2 + c

    0 = 25 a + 25

    - 25 a = 25 Divide both sides by - 25

    a = 25 / - 25

    a = - 1


    Also for x = 5 y = 0

    0 = a * 5 ^ 2 + c

    0 = 25 a + 25

    - 25 a = 25 Divide both sides by - 25

    a = 25 / - 25

    a = - 1


    Equation of this parabola is :

    y = - x ^ 2 + 25

  • Integrated Math 1 -

    Answer A.

  • Integrated Math 1 -

    If you want to see graph go on:

    rechneronline.de

    In blue rectangle type :

    - x ^ 2 + 25

    Set :

    Range x-axis from - 10 to 10

    Range x-axis from - 10 to 40

    and click option Draw

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E) The …
  2. math

    A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E) The …
  3. algebra

    6. Find the equation of each parabola described below. a) parabola with vertex (0,0) and the focus (0,7) b) parabola with focus (-3,0) and directrix x=3 c) parabola with vertex (3,3) and directrix x=-1 d) parabola with focus (-2,-1) …
  4. math

    An equitorial triangles is inscribed in the parabola y^2=4ax, where one vertex is vertex of parabola. what will be the length of the side of triangle?
  5. Integrated Math 1

    Suppose a parabola has its vertex at (0, 1) and its zeros at x = -3 and x = 3. Then equals _____. A. 9-x^2 B. 1-1/9x^2 C. x^2-1 D. x^2-9
  6. Integrated Math 1

    Suppose a parabola has its vertex at (0, 1) and its zeros at x = -2 and x = 2. Then equals _____. A. 1-1/4x^2 B. 4-x^2 C. X^2-1 D. X^2-4
  7. algebra

    Suppose a parabola has a vertex (-4,7) and also passes through the point (-3,8) Write the equation of the parabola in vertex form. f(x)=a(x-h)^2+k I believe h=-4 k=7 Not sure what to do from here.
  8. Math

    1.) If a = 2 and the vertex of a parabola is (3, -4), will there be a minimum or maximum value for the parabola?
  9. algebra

    Suppose a parabola has vertex (-4,7) and also passes through the point (-3,8), write the equation of the parabola in vertex form.
  10. Algebra

    Can you please help me with the below question: The vertex of a parabola is located at (-12, -1). The parabola also passes through the point (-10, 5). Write the equation of this parabola in both vertex form and standard form. Vertex …

More Similar Questions