!!! PLEASE HELP FAST !! please help me with one a two :)
1 answer:
Answer:
<h3>Question 1</h3><u>Function given:</u>
- y = x² + 4x - 4
<u>In the vertex form:</u>
- y = x² + 4x + 4 - 8 = (x + 2)² - 8
Axis of symmetry is the vertical line passing through the vertex.
<u>The vertex is</u>
- (-2,-8)
<u>Axis of symmetry is </u>
- x = -2
<u>y- intercept is </u>
- x = 0 ⇒ y = -4, so the point (0, -4)
<u>Two other points are</u>
- x = 1 ⇒ y = (1 + 2)² - 8 = 9 - 8 = 1, the point is (1, 1)
- x = -1 ⇒ y = (-1 + 2)² - 8 = 1 - 8 = -7, the point is (-1, -7)
<em>See the graph with all the points plotted</em>
<h3>Question 2</h3><u>Function given:</u>
- y + 2x² - 4x - 6 = 0
<u>In standard form:</u>
- y = -2x² + 4x + 6
<u>In vertex form:</u>
- y = - 2x² + 4x - 2 + 8 = -2(x - 1)² + 8
<u>The vertex:</u>
- (1, 8)
<u>Axis of symmetry is </u>
- x = 1
<u>y - intercept </u>
- x = 0 ⇒ y = -2(-1)² + 8 = -2 + 8 = 6, the point is (0, 6)
<u>Two other pints:</u>
- x = -1 ⇒ y = -2(-1 - 1)² + 8 = -8 + 8 = 0, the point is (-1, 0)
- x = 2 ⇒ y = -2(2 - 1)² + 8 = -2 + 8 = 6, the point is (2, 6)
<em>The graph is attached with the points plotted.</em>
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Remember that the equation of a circle is:
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.
Complete the square. We must do this for x² - 6x and y² - 10y separately.
x² - 6x
Divide -6 by 2 to get -3.
Square -3 to get 9. Add 9,
x² - 6x + 9
Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.
Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.
y² - 10y
Divide -10 by 2 to get -5.
Square -5 to get 25.
Add 25 on both sides.
Factor y² - 10y + 25 to get (y - 5)²
Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)
Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.
Complete the square. We must do this for x² - 6x and y² - 10y separately.
x² - 6x
Divide -6 by 2 to get -3.
Square -3 to get 9. Add 9,
x² - 6x + 9
Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.
Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.
y² - 10y
Divide -10 by 2 to get -5.
Square -5 to get 25.
Add 25 on both sides.
Factor y² - 10y + 25 to get (y - 5)²
Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)
Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.