1 .What is the equation of the line through (1,2) and (3, -1)?
Answer:
To get the equation of this line, I need → a. a point and b. a slope
Step 1 first, find the slope:
M = y2 – y1/ x2 –x1
M = -1/3 -2/1
M = -3/2
Step 2: using the point slop formula→
Using one of the given points,
(1, 2) and m = -3/2
Y -2 = -3x/2 – 3/2
Y = -3x/2 +7/2
The final answer is
Y = -3x/2 +/2
2. What is the vertex of f(x) = x2 – 6x + 3?
Answer:
In order to find the vertex of f(x) = x² -6x +3→ I first need to find the x coordinate value of vertex. The formula →x = -b/2a and start with given equation as follows→
Y = x²-6x+2, → I can see that → a = 1, b = -6, c = 2
X = - (-6)/2x (1) in this case I insert a = 1, b = -6
X =6/2x (1) which negated -6 → to get +6
X = 6/2 → multiply → 2 and 1 to get → 2.*…show more content…*

So the x- coordinate of the vertex is x =2. Now the x - coordinate value of the vertex this time I can use to find the y – coordinate of the vertex. Y = x² - 6x +2 → start with the given equation Y = (3)² - 6x (3) +2 → plug in x = 3 Y = 1 x (9) – 6x (3) + 2 → square 3 to get 9. Y 9 – 18 + 2 multiply -6 and 3 to get -18 Y = 7 combine line terms At this point the y – coordinate of the vertex is y = -7 Finally the vertex is (3, -7) 3. Using points, straight lines, and possibly the curve of a parabola, construct a piecewise function whose graph looks like a smiling

So the x- coordinate of the vertex is x =2. Now the x - coordinate value of the vertex this time I can use to find the y – coordinate of the vertex. Y = x² - 6x +2 → start with the given equation Y = (3)² - 6x (3) +2 → plug in x = 3 Y = 1 x (9) – 6x (3) + 2 → square 3 to get 9. Y 9 – 18 + 2 multiply -6 and 3 to get -18 Y = 7 combine line terms At this point the y – coordinate of the vertex is y = -7 Finally the vertex is (3, -7) 3. Using points, straight lines, and possibly the curve of a parabola, construct a piecewise function whose graph looks like a smiling

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