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Mathematics

2 answers:

polet [3.4K]3 years ago

8 0

Answer:

y = (x -3)² -2

Step-by-step explanation:

The vertex form of the equation of a parabola is ...

y = a(x -h)² + k

for vertex (h, k) and vertical scale factor "a".

Your graph shows the vertex to be at (x, y) = (3, -2). Note that one unit either side of the vertex, the graph goes up one unit. The number of vertical units difference from the vertex is the value of "a", so it is 1 for this parabola.

That means the equation is ...

y = 1·(x -3)² -2

or, more simply, ...

y = (x -3)² -2 . . . . . . . matches the 3rd choice

_____

Please note that if "a" is negative, the parabola will open downward. This one opens upward, so you can immediately reject the first two answer choices.

Luba_88 [7]3 years ago

4 0

Answer:c. Y=(x-3)^2-2

Step-by-step explanation: y=(x-3)^2-2

Y=x^2-6x+7

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The graph of a line and an exponential can intersect twice, once or not at all. Describe the possible number of intersections fo

Katyanochek1 [597]

Answer:

c) parabola and circle: 0, 1, 2, 3, 4 times

d) parabola and hyperbola: 1, 2, 3 times

Step-by-step explanation:

c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.

d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.

If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.