A candy store keeps track of its sales during the month of October. Below is the number of sales for the first, second, third an
d fourth week of the month.
Week 1 ; 2 ; 3 ; 4
Candy Sales 97 ; 168 ; 259 ; 375
Which graph could represent the data shown below?
Week 1 ; 2 ; 3 ; 4
Candy Sales 97 ; 168 ; 259 ; 375
Which graph could represent the data shown below?
2 answers:
From the attached diagram you can see that regression that best fits given data is quadratic (not linear).
- option 1 is false, because it gives linear regression;
- option 2 is true, it gives graph, similar to quadratic parabola;
- options 3 and 4 are false, because graphs are decreasing.
Answer: correct choice is B.
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The equation is 
.
We are looking for a function with a vertex above the x-axis and a function that opens upward (has coefficient a > 0).
The first function opens downward and intersects the x-axis. The second function has a vertex below the x-axis. The third function satisfies our requirements. The fourth function has a vertex on the x-axis.
We can solve this algebraically with the knowledge that the real solutions of a quadratic are its x-intercepts. If there are no x-intercepts (because it lies entirely above or below the x-axis), then there are no real solutions. This is true when the discriminant
. You can see that from the quadratic formula. This holds true for both answers A and C, so to find the correct one, we remember that when the coefficient a of the 
term is positive, the graph opens upwards, so we choose C.
We are looking for a function with a vertex above the x-axis and a function that opens upward (has coefficient a > 0).
The first function opens downward and intersects the x-axis. The second function has a vertex below the x-axis. The third function satisfies our requirements. The fourth function has a vertex on the x-axis.
We can solve this algebraically with the knowledge that the real solutions of a quadratic are its x-intercepts. If there are no x-intercepts (because it lies entirely above or below the x-axis), then there are no real solutions. This is true when the discriminant