Answer:
y = 2(x - 2)² + 3 vertex form
y = 2x² - 8x + 11 standard form
Step-by-step explanation:
Vertex form
y = a(x - h)² + k
(h, k) = (2, 3)
y = a(x - 2)² + 3
To find "a" plug in the y-intercept (0, 11)
11 = a(-2)² + 3
11 = 4a + 3
Subtract 3 from both sides
8 = 4a
a = 2
y = 2(x - 2)² + 3
Expand
y = 2(x² - 4x + 4) + 3
y = 2x² - 8x + 11
The equation of the line is given as
A straight line equation is given in the form
where
is the gradient and
is the y-interest.
We need to rearrange
to make
the subject.
⇒ from here we can read the gradient and the y-intercept. The gradient,
and
.
<span>A line that is parallel to
will have the same gradient,
but different y-intercept. One example of equation of a line that is parallel to
is
</span>
True, every number is a complex number.
I hope this helps. :)
Wheres the answer choices
I think instead of "conjunction" it should say "conjecture"
Anyways, draw out a quadrilateral (see figure 1 attached). It can be any figure with 4 sides. Label the angles as A, B, C and D. The conjecture to prove is that A+B+C+D = 360. In other words, the sum of the four angles of any quadrilateral is always 360 degrees.
Draw a segment from A to C. This segment will cut the quadrilateral into two triangles. Re-label angle A to angle E and F. Do the same for angle C (label it G and H). Essentially, angle A = E+F and angle C = G+H.
See figure 2. Notice how I've color-coded things. The blue angles correspond to one triangle while the red angles correspond to the other triangle.
Since we know that three angles of a triangle always add to 180, we can say
B+G+E = 180
F+D+H = 180
Add the two equations (add left side separately; do the same for the right side)
Doing so leads to
B+G+E+F+D+H = 180+180
(E+F) + B + (G+H) + D = 360
A+B+C+D = 360
Which proves the conjecture
