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A paint can is dropped from the top of a building 51.84 feet above the ground. So, 51.84 feet is the can's maximum height. After 0.5 seconds, the can is 47.84 feet above the ground. The can hits the ground 1.8 seconds after it is dropped.
Let
f(x) be the height (in feet) of the can
x seconds after it is dropped. Then, the function
f is guadratic. (Its graph is a parabola with vertex (
0,51.84).) Write an equation for the quadratic function
f.

A paint can is dropped from the top of a building $51$ . $84$ feet above the ground. So, $51$ . $84$ feet is the can's maximum height. After $0$ . $5$ seconds, the can is $47$ . $84$ feet above the ground. The can hits the ground $1$ . $8$ seconds after it is dropped. $\newline$ Let $f(x)$ be the height (in feet) of the can $x$ seconds after it is dropped. Then, the function $f$ is guadratic. (Its graph is a parabola with vertex ( $0,51.84)$ .) Write an equation for the quadratic function $f$ .

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A paint can is dropped from the top of a building

51

.

84

feet above the ground. So,

51

.

84

feet is the can's maximum height. After

0

.

5

seconds, the can is

47

.

84

feet above the ground. The can hits the ground

1

.

8

seconds after it is dropped.

\newline

Let

f(x)

be the height (in feet) of the can

x

seconds after it is dropped. Then, the function

f

is guadratic. (Its graph is a parabola with vertex (

0,51.84)

.) Write an equation for the quadratic function

f

.

Identify Vertex: Identify the vertex of the parabola, which is the initial position of the can when dropped.
Find 'a' Value: Use the point $(0.5, 47.84)$ to find the value of 'a' in the quadratic equation $f(x) = ax^2 + bx + c$ . Since we know the vertex, we can use the vertex form of a quadratic equation, $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex.
Write Equation: Write the equation using the value of $a$ found.
Check Validity: Check if the equation is correct by substituting $x = 1.8$ to see if it hits the ground ( $f(x) = 0$ ).

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