Maths-
General
Easy

Question

Write a function in vertex form for the parabola shown below :

hintHint:

The vertex form of a quadratic function is
f(x) = a(x – h)2 + k
Where a, h, and k are constants. Here, h represents horizontal translation, a represents vertical translation and (h,k) is the vertex of the parabola. Also, a represents the Vertical stretch/shrink of the parabola and if a is negative, then the graph is reflected over the x-axis.
 

The correct answer is: Hence, the vertex form of the given parabola is y = 2(x+1)2 - 3


    Let’s say that the equation of the parabola is y = a(x – h)2 + k
    As we can see from the figure that the vertex of the parabola is (-1,-3). So, h = -1 and k = -3
    y = a(x + 1)2 - 3
    We can also coordinate on the parabola i.e. (0,-1) which will help us to find a
    -1 = a(0+1)2 - 3
    -1 = a -3
    a = 2
    So, the equation becomes y = 2(x+1)2 - 3
    Final Answer:
    Hence, the vertex form of the given parabola is y = 2(x+1)2 - 3

    Related Questions to study

    General
    Maths-

    The height of a ball thrown into the air is a quadratic function of time, the ball is thrown from a height of 6 ft above the ground. After 1 second, the ball reaches its maximum height of 22 ft above the ground, write the equation of the function in vertex form.

    The height of a ball thrown into the air is a quadratic function of time, the ball is thrown from a height of 6 ft above the ground. After 1 second, the ball reaches its maximum height of 22 ft above the ground, write the equation of the function in vertex form.

    Maths-General
    General
    Maths-

    Solve Graphically :
    X+Y= -1
    Y-2X=-4

    Solve Graphically :
    X+Y= -1
    Y-2X=-4

    Maths-General
    General
    Maths-

    Two poles 30m and 15 m high stand upright in a ground. If their feet are 36m apart, find the distance between their tops?

    Two poles 30m and 15 m high stand upright in a ground. If their feet are 36m apart, find the distance between their tops?

    Maths-General
    parallel
    General
    Maths-

    How can you determine the values of h and k from the graph shown? Write the function for the parabola.

    How can you determine the values of h and k from the graph shown? Write the function for the parabola.

    Maths-General
    General
    Maths-

    To graph the function f(x)= (x-5)2 -8, a student translates the graph of the quadratic parent function 5 units right and 8 units down. Can a student produce the graph of f(x)= 2(x+3)2 -5 by simply translating the quadratic parent function? Explain

    To graph the function f(x)= (x-5)2 -8, a student translates the graph of the quadratic parent function 5 units right and 8 units down. Can a student produce the graph of f(x)= 2(x+3)2 -5 by simply translating the quadratic parent function? Explain

    Maths-General
    General
    Maths-

    The graph shown is a translation of the graph of f(x)=2x2. Write the function for the graph in vertex form

    The graph shown is a translation of the graph of f(x)=2x2. Write the function for the graph in vertex form

    Maths-General
    parallel
    General
    Maths-

    The diagonals of a rhombus are 12 cm and 9 cm long. Calculate the length of one side of a rhombus?

    The diagonals of a rhombus are 12 cm and 9 cm long. Calculate the length of one side of a rhombus?

    Maths-General
    General
    Maths-

    The graph of h is the graph of g(x)= (x-2)2+6 translated 5 units left and 3 units down.
    a. Describe the graph of h as a translation of the graph of f(x)= x2
    b. Write the function h in vertex form.

    The graph of h is the graph of g(x)= (x-2)2+6 translated 5 units left and 3 units down.
    a. Describe the graph of h as a translation of the graph of f(x)= x2
    b. Write the function h in vertex form.

    Maths-General
    General
    Maths-

    In ∆ABC, ∠ABC = 90° AD is the median to BC and CE is the median to AB. If AC = 5 cm and AD =fraction numerator 3 square root of 5 over denominator 2 end fraction  cm, find CE.

    In ∆ABC, ∠ABC = 90° AD is the median to BC and CE is the median to AB. If AC = 5 cm and AD =fraction numerator 3 square root of 5 over denominator 2 end fraction  cm, find CE.

    Maths-General
    parallel
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function
    f(x)= x2+2

    Find the vertex, axis of symmetry and sketch the graph of the function
    f(x)= x2+2

    Maths-General
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x2 -5

    Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x2 -5

    Maths-General
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function g(x)= x2 -1

    Find the vertex, axis of symmetry and sketch the graph of the function g(x)= x2 -1

    Maths-General
    parallel
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x2+0.5
     

    Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x2+0.5
     

    Maths-General
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function.
    F(x) = -2(x + 1)2 + 5

    Find the vertex, axis of symmetry and sketch the graph of the function.
    F(x) = -2(x + 1)2 + 5

    Maths-General
    General
    Maths-

    Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x2-2.25

    Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x2-2.25

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.