Annette throws a ball upward. If this graph describes the trajectory of the ball, what is its corresponding function?

f(x) = x2 − 6x + 25

f(x) = -1.89x2 + 11.33x + 30

f(x) = 1.89x2 − 11.33x + 4

f(x) = -x2 + 6x + 4

f(x) = x2 + 6x + 17

Question

Annette throws a ball upward. If this graph describes the trajectory of the ball, what is its corresponding function?


f(x) = x2 − 6x + 25



f(x) = -1.89x2 + 11.33x + 30



f(x) = 1.89x2 − 11.33x + 4



f(x) = -x2 + 6x + 4



f(x) = x2 + 6x + 17

anonymous · Answer

attachment

anonymous · Answer

will give medal and fan

ddcamp · Answer

Let's start by narrowing down the choices.

ddcamp · Answer

Just like lines, parabolas have a y-intercept. The y intercept is the value at x=0, and it corresponds to the term in the function without an x attached to it.

What's the y-intercept of this graph?

anonymous · Answer

Go on graph.tk and type each one in, the one that comes out to the same result is the correct answer

anonymous · Answer

4

ddcamp · Answer

Good!
That already narrows it down to 2 choices.

ddcamp · Answer

The next thing to do with parabolas is check the direction that it opens.
If the top is open, the coefficient on the x^2 term is positive.
If the bottom is open, the coefficient on the x^2 term is negative.

anonymous · Answer

so its negative

ddcamp · Answer

Yup!

ddcamp · Answer

While we have enough now for this problem, here's something else that might be useful:

Given a quadratic function:
$$y = ax^2 + bx +c$$
The x-coordinate of the vertex is at:
$$x = -\frac{b}{2a}$$

anonymous · Answer

thank you for your help