Answer:
Step-by-step explanation:
Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:
Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:
The reason we do this is to create a perfect square binomial on the left:
(obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:
This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.
I believe question 3 is B and question 4 is B
I would do this by first listing the multiples of 6 until I start to see a pattern with the one's digit.
6x0=0
6x1=6
6x2=12
6x3=18
6x4=24
6x5=30
6x6=36
6x7=42
6x8=48
...
The digits in bold are the one's digits so those are the only ones we really care about. If you list just them it looks like: 0,6,2,8,4,0,6,2,8
Notice how the first set of 5 numbers seems as though it repeats in the 6th, 7th, and 8th numbers. This probably means the pattern continues infinitely so the first 5 numbers are all the one's digits that can come from multiples of 6. Thus your answer is: 0,6,2,8,or 4
Jony is 2 now and is 2x older than Chika. So Chika is 1 year old. This means Chika is 1 year younger than Jony. When Jony is 30, Chika is 29
<span><u><em>The correct answer is:</em></u>
180</span>°<span> rotation.
<u><em>Explanation: </em></u>
<span>Comparing the points D, E and F to D', E' and F', we see that the x- and y-coordinates of each <u>have been negated</u>, but they are still <u>in the same position in the ordered pair. </u>
<u>A 90</u></span></span><u>°</u><span><span><u> rotation counterclockwise</u> will take coordinates (x, y) and map them to (-y, x), negating the y-coordinate and swapping the x- and y-coordinates.
<u> A 90</u></span></span><u>°</u><span><span><u> rotation clockwise</u> will map coordinates (x, y) to (y, -x), negating the x-coordinate and swapping the x- and y-coordinates.
Performing either of these would leave our image with a coordinate that needs negated, as well as needing to swap the coordinates back around.
This means we would have to perform <u>the same rotation again</u>; if we began with 90</span></span>°<span><span> clockwise, we would rotate 90 degrees clockwise again; if we began with 90</span></span>°<span><span> counter-clockwise, we would rotate 90 degrees counterclockwise again. Either way this rotates the figure a total of 180</span></span>°<span><span> and gives us the desired coordinates.</span></span>
