• Angles DXC and AXB form a vertical pair, so they are congruent and have the same measure.
• ∆ABD is isosceles, since it's given that AD and BD are congruent. This means the "base angles" BAD and ABD have the same measure; call this measure <em>x</em>.
• The measure of angle ADB can be computed by using the inscribed angle theorem, which says
m∠ADB = 1/2 (100°) = 50°
(that is, it's half the measure of the subtended arc AB whose measure is 100°)
• The interior angle to any triangle sum to 180° in measure. So we have in ∆ABD,
m∠ADB + 2<em>x</em> = 180°
Solve for <em>x</em> :
50° + 2<em>x</em> = 180°
2<em>x</em> = 130°
<em>x</em> = 65°
• Use the inscribed angle theorem again to find the measure of angle BAC. This will be half the measure of the subtended arc BC, so
m∠BAC = 1/2 (50°) = 25°
• Now in ∆ABX, we have
m∠AXB + 25° + 65° = 180°
m∠AXB = 90°
Hence m∠DXC = 90°.
Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) =
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = () + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases