Write a linear function f withe the values f (10) = 5 and f (2) = -3
1 answer:
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Answer:
Graph in the image attached.
Step-by-step explanation:
Using the model of a linear equation, we have:
'b' is the y-intercept of the equation, that is, the inicial value of G, when D = 0.
So if David starts the trip with 14 gallons of gas, we have b = 14.
'a' is the slope of the line, that is, an increase of 1 in the value of D causes an increase of 'a' in the value of G.
So if the car uses one gallon every 20 miles, the value of a is -1/20 (an increase of 20 in D causes a decrease of 1 in G).]
So our equation is:
The graph of this equation is in the image attached.
Answer:
A. y = (x -7)² +9
B. y = -(x +3)² -11
C. minimum, (7, 9)
D. maximum, (-3, -11)
Step-by-step explanation:
The general steps to rewriting the function in vertex form are ...
1. factor out the leading coefficient (if not 1) from the first two terms
2. add inside parentheses the square of half the x coefficient; subtract the same amount outside parentheses. The factor in front of the parentheses must be taken into account when adding the same amount outside.
3. rewrite the content of parentheses as a square, collect terms outside parentheses.
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A. y = x² -14x +58
y = (x² -14x) +58 . . . . . . . . . . step 1
y = (x² -14x +49) +58 -49 . . . step 2
y = (x -7)² +9 . . . . . . . . . . . . . step 3
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B. y = -x² -6x -20
y = -(x² +6x) -20
y = -(x² +6x +9) -20 -(-9)
y = -(x +3)² -11
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C. In vertex form, the function for vertical scale factor "a" and vertex (h, k) looks like ...
y = a(x -h)² +k
When a < 0, the vertex is a maximum (the graph opens downward); when a > 0, the vertex is a minimum (the graph opens upward).
The function of part A has a minimum at the vertex (7, 9). 9 is the minimum value.
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D. The function of part B has a maximum at the vertex (-3, -11). -11 is the maximum value.
