Tiffany is solving an equation where both sides are quadratic expressions. She sets each quadratic equation equal to y and graph
s the resulting system. If the graph of one quadratic opens upward and the other opens downward, what is the greatest possible number of intersections for these graphs?
2 answers:
Answer:
Step-by-step explanation:
There are 3 possibilities for the graph as shown in the figure.
(a) having zero intersection
(b) having one intersection point (touching point)
(c) having two intersection points.
So, the greatest possible number of intersections for these graphs is 2 as shown in figure (c).
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Answer:
a)
b)
c)
Step-by-step explanation:
Given the curve
a) If the x-coordinate of P is , then the y-coordinate is
so point P has coordinates
If the x-coordinate of Q is , then the y-coordinate is
so point Q has coordinates
b) The gradient of the secant RQ is
c) If then the gradient
Question is Incomplete. Complete question is given below;
Maggie brought $10 to the candy store. She will buy a certain amount of fudge. One pound of fudge costs $2.30. If p represents the amount of fudge, in pounds, Maggie buys, which expression represents the money Maggie has left after visiting the candy store?
Answer:
The expression that represent the money Maggie has left after visiting the candy store is
Step-by-step explanation:
Given:
Money Maggie brought at store = $10
Cost of 1 pound of fudge = $2.30
Let the amount of fudge be p
We need to find the amount of Money Maggie has left with after visiting the store.
The amount of Money Maggie has left with can be calculate by subtracting the amount of fudge she bought multiplied by Cost of 1 pound of fudge with Money Maggie brought at store.
The equation can be framed as;
Money left =
Hence, The expression that represent the money Maggie has left after visiting the candy store is
First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.
Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.
Now check on the boundary lines themselves. If <em>x</em> = 0, then
which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).
If <em>y</em> = 2, then
with a maximum of -5 when <em>x</em> = 1.
If <em>y</em> = 2<em>x</em>, then
with the same maximum of -5 when <em>x</em> = 1.