Question

Pls help ILL MARK BRAINLIEST

Answer 1

Answer:

a) Height of the ledge is 1.6 m.

b) roots of the equation are: $\bf d = 2$ ,  $\bf d = -1$

c) Maximum height reached = 1.8 m.

Step-by-step explanation:

a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:

$h = -0.8(0)^2 + 0.8(0) + 1.6$

⇒ $\bf h = 1.6 \space\ m$

∴ Height of the ledge is 1.6 m.

b) The x-intercepts occur where y = 0, that is when h = 0:

$-0.8d^2 + 0.8d + 1.6 = 0$

Divide both sides of the equation by -0.8:

$d^2 - d -2 = 0$

Factorizing:

⇒ $d^2 -2d + d - 2 = 0$

⇒ $d(d-2) +1 (d-2) = 0$

⇒ $(d-2)(d+1) = 0$

⇒ $d - 2 = 0$    or    $d + 1 = 0$

∴ roots are :  $\bf d = 2$   ,   $\bf d = -1$

c) To find the maximum value of a quadratic equation in the form

y = ax² + bx + c , use the formula:

max = c - (b² / 4a).

Using the formula for $h = -0.8x^2 + 0.8x + 1.6$ :

max h =  $1.6 - ( \frac{0.8^2}{4(-0.8)} )$

       = 1.8

∴ Maximum height reached = 1.8 m.

Answer 2

Answer:

  a) 1.6 m

  b) -1, 2 meters

  c) 1.8 m

Step-by-step explanation:

Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.

a) ledge height

The height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.

The height of the ledge is 1.6 meters.

b) roots

The x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...

 d = -1

  d = 2 . . . . meters

c) maximum height

The maximum height is the "h" coordinate of the vertex (d, h).

The maximum height is 1.8 meters.

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Additional comment

"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".

Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.