Please what is the vertex and the point of this graph k (×)=[2 (×+4)]^2+3
2 answers:
<span>The vertex form of a quadratic is given by </span><span>y = a(x – h)^2 + k</span><span>, where </span><span>(h, k)</span><span> is the vertex ; In your case , ( - 4 , 3 ) is the vertex ;</span>
K(x) = 2(x + 4)² + 3 k(x) = 2(x + 4)(x + 4) + 3 k(x) = 2(x² + 4x + 4x + 16) + 3 k(x) = 2(x² + 8x + 16) + 3 k(x) = 2(x²) + 2(8x) + 2(16) + 3 k(x) = 2x² + 16x + 32 + 3 k(x) = 2x² + 16x + 35 2x² + 16x + 35 = 0 x = <u>-(16) +/- √((16)² - 4(2)(35))</u> 2(2) x = <u>-16 +/- √(256 - 280)</u> 4 x = <u>-16 +/- √(-24) </u> 4<u> </u>x = <u>-16 +/- 2i√(6) </u> 4 x = -4 <u>+</u> 0.5i√(6) x = -4 + 0.5i√(6) x = -4 - 0.5i√(6) k(x) = 2x² + 16x + 35 k(-4 + 0.5i√(6)) = 2(-4 + 0.5i√(6))² + 16(-4 + 0.5i√(6)) + 35 k(-4 + 0.5i√(6)) = 2(-4 + 0.5i√(6))(-4 + 0.5i√(6)) + 16(-4) + 16(0.5i√(6)) + 35 k(-4 + 0.5i√(6)) = 2(16 - 2i√(6) - 2√(6) + 0.25i²√(36)) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 0.25i²(6)) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5i²) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√(1²)) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√(1 × 1)) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√1) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-1)) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) - 1.5) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 2(16) - 2(4i√(6)) - 2(1.5) - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 32 - 8i√(6) - 3 - 64 + 8i√(6) + 35 k(-4 + 0.5i√(6)) = 32 - 3 - 64 + 35 - 8i√(6) + 8i√(6) k(-4 + 0.5i√(6)) = 29 - 64 + 35 + 0i√(6) k(-4 + 0.5i√(6)) = -35 + 35 + 0 k(-4 + 0.5i√(6)) = 0 + 0 k(-4 + 0,5i√(6)) = 0 (x, k(x)) = (-4 + 0.5i√(6), 0) or k(x) = 2x² + 16x + 35 k(-4 - 0.5i√(6)) = 2(-4 - 0.5i√(6))² + 16(-4 - 0.5i√(6)) + 35 k(-4 - 0.5i√(6)) = 2(-4 - 0.5i√(6))(-4 - 0.5i√(6)) + 16(-4) - 16(0.5i√(6)) + 35 k(-4 - 0.5i√(6)) = 2(16 + 2i√(6) + 2i√(6) + 0.25i²√(36)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 0.25i²(6)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5i²) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1²)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1 × 1)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-1)) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) - 1.5) - 64 - 8i√(6) + 35 k(-4 - 0.45i√(6)) = 2(16) + 2(4i√(6)) - 2(1.5) - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 32 + 8i√(6) - 3 - 64 - 8i√(6) + 35 k(-4 - 0.5i√(6)) = 32 - 3 - 64 + 35 + 8i√(6) - 8i√(6) k(-4 - 0.5i√(6)) = 29 - 64 + 35 + 0i√(6) k(-4 - 0.5i√(6)) = -35 + 35 + 0 f(-4 - 0.5i√(6)) = 0 + 0 f(-4 - 0.5i√(6)) = 0 (x, k(x)) = (-4 - 0.5i√(6), 0) The point of the graph is (-4 <u>+</u> 0.5i√(6), 0), or (-4 + 0.5i√(6), 0) and (-4 - 0.5i√(6),0). The vertex of the graph is (-4, 3). <u />
You might be interested in
Answer:
D is the correct answer! Hope it hepls!
Step-by-step explanation:
Please mark brainliest!
Answer: amplitude is 5 and Period is pi/2
Step-by-step explanation:
yes ♀️
3? i’m not too sure sorry boo xxo
The perimeter of the circle is also known as the circumference that said figure out what the diameter is and multiply that by pi (3.14)
Answer:
D?
Step-by-step explanation: