MHB Finding the vertex of a quadratic and the product of two complex numbers

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The discussion focuses on finding the vertex of the quadratic function f(x) = -2x^2 - 8x + 3 and multiplying two complex numbers. The initial answer provided for the vertex was (-2, 0), but it was corrected to (-2, 11) after further calculations. The correct method involved using the vertex formula x = -b/(2a) and substituting back to find the y-coordinate. The multiplication of the complex numbers (6 - 5i)(4 + 3i) was confirmed to yield the correct answer of 39 - 2i. The conversation emphasizes the importance of verifying calculations in algebraic problems.
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Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

11) Find the vertex of f(x) = -2x^2 - 8x + 3 algebraically.

My Answer: (-2,0)

12) Multiply and simplify: (6 - 5i) (4 + 3i)

My Answer: 39 - 2i
 
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Re: Please check my answers - 6

drop said:
Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

11) Find the vertex of f(x) = -2x^2 - 8x + 3 algebraically.

My Answer: (-2,0)

I get $(-2, 11)$. Now can you help me by explaining to us how did you arrive at $(-2, 0)$ as the vertex of the function of f of x?
drop said:
12) Multiply and simplify: (6 - 5i) (4 + 3i)

My Answer: 39 - 2i

Correct.:)
 
Re: Please check my answers - 6

x = -b/(2a)

x = -(-8)/2(-2)

x = 8/-4 = -2

I think I forgot to substitute -2 for x to find out y, thanks for pointing that out! (I was thinking of x intercepts) After solving for y, I got (-2,11) Thank you
 
Re: Please check my answers - 6

Yes...and as you can see, $f(-2)=-2(-2)^2-8(-2)+3=11$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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