The height y (in feet) of a ball thrown by a child is where x is the horizontal distance in feet from the point at which the ball is thrown a).how high is the ball when it leaves the child's handb).what is the maximum high of the ballc).how far from the child does the ball strike the ground

a) 3 ft

b) 67 ft

c) 64.741 ft.

Step-by-step explanation:

Let as consider the height y (in feet) of a ball thrown by a child is

where x is the horizontal distance in feet from the point at which the ball is thrown

.

(a)

We need to find the initial height of the ball.

Substitute x=0 in the given equation.

Therefore, the height of ball is 3 ft when it leaves the child's hand.

(b)

If a quadratic equation is defined as

then the vertex of the function is

In the given equation and b=4. So,

Substitute x=32 in the given equation.

The vertex of the parabola is (32,67). So, the maximum height of the ball is 67 ft.

(c)

The height of the ball is zero when it touch the ground.

Substitute y=0 in the given function.

Using quadratic formula, we get

The distance can not be negative. So the ball will touch the ground at the distance of 64.741 ft.

step-by-step explanation:

it's 15

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.