Question

Jeremy and Arnold are working on a project for math class in which they are to identify the quadratic equation that represents a rain gauge that sits off the ground. Graph each of the equations and then determine which one could represent the position of the rain catcher that sits above the ground. The x-axis represents the ground.
y = x2 + 11x + 24 2. y = –x2 – 6x – 8



Direction of Parabola: ______ Direction of Parabola: ______

Location of vertex with respect Location of vertex with respect
to the x axis: _____________ to the x axis: _____________

Determine if the graph depicts Determine if the graph depicts
the rain gauge. ___________ the rain gauge. ___________

Why or why not? ___________ Why or why not? ___________
_________________________ _________________________
_________________________ _________________________



y = x2 – 2x + 3 4. y = x2 + 4x + 4



Direction of Parabola: ______ Direction of Parabola: ______

Location of vertex with respect Location of vertex with respect
to the x axis: _____________ to the x axis: _____________

Determine if the graph depicts Determine if the graph depicts
the rain gauge. ___________ the rain gauge. ___________

Why or why not? ___________ Why or why not? ___________
_________________________ _________________________
_________________________ _________________________


y = 3x2 + 21x + 30



Direction of Parabola: ______

Location of vertex with respect
to the x axis: _____________

Determine if the graph depicts
the rain gauge. ___________

Why or why not? ___________
_________________________
_________________________

Answer 1

Answer:

The parabola generated by the expression :

$y=x^2-2x+3$

is the one that better represents a rain gauge above the ground.

Step-by-step explanation:

The function:

a) $y=x^2+11x+24$

Direction of parabola: branches pointing up

Location of vertex relative to x-axis: below

So, the parabola doesn't depict a rain gauge off the ground

b) $y=-x^2-6x-8$

Direction of parabola: branches pointing down

Location of vertex relative to x-axis: above

So, the parabola doesn't depict a rain gauge off the ground

c) $y=x^2-2x+3$  

Direction of parabola: branches pointing up

Location of vertex relative to x-axis: two units above

So, the parabola depicts a rain gauge off the ground

d) $y=x^2+4x+4$

Direction of parabola: branches pointing up

Location of vertex relative to x-axis: right on the x-axis

So, the parabola doesn't depict a rain gauge off the ground (this is sitting on the ground)

e) $y=3x^2+21x+30$

Direction of parabola: branches pointing up

Location of vertex relative to x-axis:  below

So, the parabola doesn't depict a rain gauge off the ground