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Contact [7]
3 years ago
14

Write the equation of the parabola that has the vertex at point (2,7) and passes through the point (−1,3).

Mathematics
1 answer:
mariarad [96]3 years ago
8 0
Step One
Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the  2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two
Use the point to solve for a.
y = a(x - 2)^2 + 7
When x = - 1
Then y = 3

3 = a(-1 - 2)^2 + 7                combine -1 with - 2
3 = a (-3)^2 + 7
3 = 9a + 7                            Subtract 7 from both sides
3 - 7 = 9a
-4 = 9a                                 Divide by 9.
a = -4/9 
or                                
a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer
y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1
The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.

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8 0
3 years ago
What’s the absolute value of 8
Anuta_ua [19.1K]

Answer:

8

Step-by-step explanation:

Absolute value is always the positive value of a number.

8 0
3 years ago
Read 2 more answers
Charles drew a plan for a rectangular piece of
dalvyx [7]

The fourth coordinate of rectangular piece of material is (2.8 , -2.7)

According to the question,

Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).

As we know , the opposite sides of rectangle are equal

If we locate these coordinates in our graph and join them

Length of rectangle will be = 2.8+1.4 = 4.2cm

Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm

So, the fourth coordinate should lie 6.4cm far from  (2.8,3.7)

Subtracting 6.4 from y-axis,

Fourth coordinate = 3.7 - 6.4

= -2.7

Therefore , The fourth side of rectangle = (2.8 , -2.7)

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4 0
1 year ago
How would you match these up?
TEA [102]
<h3>Answer: Bottom right corner (ie southeast corner)</h3>

This 3D solid is a strange sideways bowl shape. Each cross section is a ring to show the empty space.

======================================================

Explanation:

Check out the diagram below. The graph was created with GeoGebra. We have y = x^2 in red and x = y^2 in blue.

The gray region is the region between the two curves. We spin this gray region around the horizontal green line y = 1 to generate the answer mentioned above.

Note how (1,1) is a fixed point that does not move as this is on the line y = 1. Every other point moves to sweep through 3D space to create the solid figure. One way you can think of it is to think of propeller blades. Or you can think of a revolving door (the door is "flat" so to speak, but it sweeps out a 3D solid cylinder).

5 0
3 years ago
A 1-liter bottle of orange juice used to cost $2.85 at a food market. Its price has increased; the new price is 110 percent of t
AfilCa [17]

Answer:

The new price of the bottle is $ 3.14.

Step-by-step explanation:

Given,

Original price of 1-liter bottle of orange juice  = $ 2.85,

Since,  the new price is 110 percent of the original price.

Thus, the new price of the bottle = 110 % of the $ 2.85

=\frac{110\times 2.85}{100}

=\frac{313.5}{100}

=3.135\approx 3.14

Hence, the new price of the bottle is $ 3.14.

5 0
3 years ago
Read 2 more answers
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