Maths-
General
Easy

Question

Deshawn and Chris are playing soccer. Chris takes a shot on goal. Deshawn is 3 ft in Infront of the goal and can reach the top of the 8 ft goal when standing directly beneath it. Can he block the shot from his current position without moving or jumping?

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, Chris would score if the ball isn't blocked by Shawn because the height of the ball is lower than the height of the goal


    Solution
    Let’s say the path of the ball is represented by a parabolic equation y = a(x – h)2 + k
    We know that at x = 2, y = 1.2. So putting the values
    1.2 = a(2 - h)2 + k
    As the vertex of the parabola is given as (16,11). So h = 16 and k = 11
    1.2 = a(2-16)2 + 11
    1.2 = 196a+11
    196a = - 9.8
    a = - 0.05
    S0, equation of the parabola is y = -0.05(x – 16)2 +11 = f(x)
    Distance of Chris from goal = 25ft
    Height of goal = 8ft
    The goal can be scored if the ball isn’t blocked and if the ball travels a distance of 25 ft towards the goal and the elevation of the ball isn't greater than 8 ft, then Chris will score.
    Put x = 25 in the equation and see if f(x) < 8 feets
    f(25) = - 0.05(25 - 16)² + 11
    f(25) = - 0.05(9)² + 11
    f(25) = - 0.05  81 + 11
    f(25) = - 4.05 + 11
    f(25) = 6.95 ft < 8 ft
    Final Answer:
    Hence, Chris would score if the ball isn't blocked by Shawn because the height of the ball is lower than the height of the goal

    Related Questions to study

    General
    Maths-

    Is the triangle whose sides are 17 cm, 15 cm and 8 cm long right-angled?

    Is the triangle whose sides are 17 cm, 15 cm and 8 cm long right-angled?

    Maths-General
    General
    Maths-

    How can the vertex form of a quadratic function help you sketch the graph of the function?

    How can the vertex form of a quadratic function help you sketch the graph of the function?

    Maths-General
    General
    Maths-

    A table of values for the quadratic function g is shown, Do the graphs of the functions g and f(x)= 3(x-1)2 +2 have the same axis of symmetry? Explain.

    A table of values for the quadratic function g is shown, Do the graphs of the functions g and f(x)= 3(x-1)2 +2 have the same axis of symmetry? Explain.

    Maths-General
    parallel
    General
    Maths-

    A tree 90 m high broke at a point but did not separate. Its top touched the ground at a distance of 27 m from its base. Find the height of the point from the ground, at which the tree broke?

    A tree 90 m high broke at a point but did not separate. Its top touched the ground at a distance of 27 m from its base. Find the height of the point from the ground, at which the tree broke?

    Maths-General
    General
    Maths-

    Solve Graphically :
    3X-Y-2=0
    2X+Y-8=0

    Solve Graphically :
    3X-Y-2=0
    2X+Y-8=0

    Maths-General
    General
    Maths-

    Solve Graphically :
    2X+3/y = 3
    3X+7/y = 2

    Solve Graphically :
    2X+3/y = 3
    3X+7/y = 2

    Maths-General
    parallel
    General
    Maths-

    In right angled triangle ∠ABC, ABC = 90° and CD = 2BD. If AB = 12 cm and AC = 15 cm, find AD.



     

    In right angled triangle ∠ABC, ABC = 90° and CD = 2BD. If AB = 12 cm and AC = 15 cm, find AD.



     

    Maths-General
    General
    Maths-

    Solve Graphically :
    X+Y=-2
    2X-Y=5

    Solve Graphically :
    X+Y=-2
    2X-Y=5

    Maths-General
    General
    Maths-

    Solve graphically :
    2X+5Y=19
    2X-5Y+11=0

    Solve graphically :
    2X+5Y=19
    2X-5Y+11=0

    Maths-General
    parallel
    General
    Maths-

    How are the form and graph of f(x)= (x-h)2+k similar to the form and graph of f(x)=|x-h|+k? How are they different?

    How are the form and graph of f(x)= (x-h)2+k similar to the form and graph of f(x)=|x-h|+k? How are they different?

    Maths-General
    General
    Maths-

    Solve Graphically :
    4X+3Y=5
    X-2Y=-7

    Solve Graphically :
    4X+3Y=5
    X-2Y=-7

    Maths-General
    General
    Maths-

    Sarah said the vertex of the function f(x)= (x+2)2+6 is (2,6). Is she correct, Explain your answer.

    Sarah said the vertex of the function f(x)= (x+2)2+6 is (2,6). Is she correct, Explain your answer.

    Maths-General
    parallel
    General
    Maths-

    Solve Graphically :
    6Y= 5X+10
    Y= 5X-15

    Solve Graphically :
    6Y= 5X+10
    Y= 5X-15

    Maths-General
    General
    Maths-

    Graph the function : g(x)= x+ 5

    Graph the function : g(x)= x+ 5

    Maths-General
    General
    Maths-

    Graph the function f(x)= (x-2)2

    Graph the function f(x)= (x-2)2

    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.