Question

question 8 (multiple choice worth 5 points)you are training your dog to catch a frisbee. you are playing in a large field, and you are standing next to your dog when you throw the frisbee. if the path of the frisbee is $y = -x^2 + 7x + 1$ and the path of the dog is modeled by $y = 2x + 5$, will the dog catch the frisbee? if so, what are the coordinates of the point or points where they meet?yes, they intersect at the coordinates (1, 7) and (4, 13)yes, they intersect at the coordinates (1, 9) and (2, 9)yes, they intersect at the coordinates (2, 11) and (3, 11)no, the paths do not cross

Explanation:

Step1: Set equations equal

Set $2x + 5 = -x^2 + 7x + 1$

Step2: Rearrange to quadratic form

$x^2 - 5x + 4 = 0$

Step3: Factor the quadratic

$(x-1)(x-4) = 0$

Step4: Solve for x-values

$x=1$ or $x=4$

Step5: Find corresponding y-values

For $x=1$: $y=2(1)+5=7$
For $x=4$: $y=2(4)+5=13$

Answer:

Yes, they intersect at the coordinates (1, 7) and (4, 13)