You use the pythagorean theorem to calculate the missing sides.
formula: a^2+b^2=c^2
a=leg, b=leg, c=hypotenuse.
substitute the lengths in and solve for the missing length.
1. 5^2+12^2=c^2 simplify exponents
25+144=c^2 add
169=c^2 square root both sides
a.13
2. 8^2+b^2=10^2
b.6
3. 15^2+20^2=c^2
b.25
4. Distance formula 5sqrt2
c.7
the equation of a parabola in
vertex form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
a
(
x
−
h
)
2
+
k
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−
where
(
h
,
k
)
are the coordinates of the vertex and a
is a multiplier
to obtain this form
complete the square
y
=
x
2
+
2
(
4
)
x
+
16
−
16
+
14
⇒
y
=
(
x
+
4
)
2
−
2
←
in vertex form
⇒
vertex
=
(
−
4
,
−
2
)
to obtain the intercepts
∙
let x = 0, in the equation for y-intercept
∙
let y = 0, in the equation for x-intercept
x
=
0
⇒
y
=
0
+
0
+
14
=
14
←
y-intercept
y
=
0
⇒
(
x
+
4
)
2
−
2
=
0
←
add 2 to both sides
⇒
(
x
+
4
)
2
=
2
take the square root of both sides
√
(
x
+
4
)
2
=
±
√
2
←
note plus or minus
⇒
x
+
4
=
±
√
2
←
subtract 4 from both sides
⇒
x
=
−
4
±
√
2
←
exact values
graph{(y-x^2-8x-14)((x+4)^2+(y+2)^2-0.04)=0 [-10, 10, -5, 5]}
Answer:
try searching it
it helps to know what linear is and how to graph it
ask a teacher if needed
Amanda table values: 3, 6, 15, 30
Mia Table values: 5, 10, 25, 50
