Question

yellow bird launches off from point 10,0. his flight path reaches a maximum height of twenty yards and lands at 42,0. what's the equation.

Answer 1

Ok so look at the basic equation in vertex form: y=a(x-h)^2 +k, where (-h, k) is the vertex. You already know k which is twenty yards, and you know that a is negative because the parabola has a maximum. You know that the vertex's x coordinate is right in between your roots, which are (10,0) and (42,0). The average of 10 and 42 is (42+10)/2 which is 26. So you know your h is 26. From the model, we can guess that the 'a' is negative one, so your equation is y=-(x-26)^2 + 20.

Answer 2

Answer:

The Equation is y = -0.1( x - 26 )² + 20

Step-by-step explanation:

Given:

Starting position of the bird = ( 10 , 0 )

Final position of the bird = ( 42 , 0 )

Maximum Height of the bird = 20 yards

To find: Equation that represent this condition.

Clearly, Birds flight path is not a straight line. It has a curved path.

So, the path bird follow is a PARABOLA.

Standard Equation of the parabola in vertex form, y = a( x - h )² + k

where ( h , k ) is the vertex of the parabola.

In our Question , vertex is the point at the highest position.

Vertex will be 20 yard above the mid point of the starting and final position.

Using Mid-Point Formula,

Mid-Point of ( 10 , 0 ) & ( 42 , 0 ) = $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{10+42}{2},\frac{0+0}{2})=(26,0)$

Now, the vertex = ( 26 , 0 + 20 ) = ( 26 , 20 )

⇒ Equation, y = a( x - 26 )² + 20

Now, we find value of by substituting value of (10 , 0) in the equation,

⇒ 0 = a( 10 - 26 )² + 20

a( -16 )² = -20

a(256) = -20

a = -20/256

a = −0.078125

a ≈ -0.1

Therefore, The Equation is y = -0.1( x - 26 )² + 20