(−112,−714) Flag question: Question 5Question 5Tips1 ptsPlot the ordered pairs (-1,-11), (2,-8), (5,-77) on the coordinate plane. Which of the following functions goes through the three given points?𝑎)𝑓(𝑥)=−4𝑥2+5𝑥−2𝑏)𝑓(𝑥)=2𝑥2+5𝑥+2𝑐)𝑓(𝑥)=−3𝑥−8Group of answer choicesNone of the functions go through given points.𝑎)𝑓(𝑥)=−4𝑥2+5𝑥−2𝑏)𝑓(𝑥)=2𝑥2+5𝑥+2𝑐)𝑓(𝑥)=−3𝑥−8
Question
(−112,−714) Flag question: Question 5Question 5Tips1 ptsPlot the ordered pairs (-1,-11), (2,-8), (5,-77) on the coordinate plane. Which of the following functions goes through the three given points?𝑎)𝑓(𝑥)=−4𝑥2+5𝑥−2𝑏)𝑓(𝑥)=2𝑥2+5𝑥+2𝑐)𝑓(𝑥)=−3𝑥−8Group of answer choicesNone of the functions go through given points.𝑎)𝑓(𝑥)=−4𝑥2+5𝑥−2𝑏)𝑓(𝑥)=2𝑥2+5𝑥+2𝑐)𝑓(𝑥)=−3𝑥−8
Solution
To determine which function goes through the three given points, we need to substitute the x and y values of each point into each function and see if the equation holds true.
Let's start with the first function 𝑓(𝑥)=−4𝑥²+5𝑥−2:
For point (-1,-11), the function becomes -4*(-1)² + 5*(-1) - 2 = -4 - 5 - 2 = -11. This matches the y-coordinate of the point, so the point lies on the function.
For point (2,-8), the function becomes -4*(2)² + 5*(2) - 2 = -16 + 10 - 2 = -8. This matches the y-coordinate of the point, so the point lies on the function.
For point (5,-77), the function becomes -4*(5)² + 5*(5) - 2 = -100 + 25 - 2 = -77. This matches the y-coordinate of the point, so the point lies on the function.
Therefore, all three points lie on the function 𝑓(𝑥)=−4𝑥²+5𝑥−2.
We can follow the same process for the other two functions, but since we've already found a function that fits all three points, the answer is 𝑓(𝑥)=−4𝑥²+5𝑥−2.
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