Can I get help with these two? I cant figure them out.
What is the vertex form of the equation?
y = - x2 +8x – 12
Simplify the expression.
(-6i)2
f(x)=- x2 +8x – 12 =-(x^2-8x+16)+4
= -(x-4)^2 +4
on the second, I assume you meant
(-6i)2
(-1^2 * 6^2 * i^2)=-36
Thank you
Of course! I'd be happy to help you with these two questions.
First, let's find the vertex form of the equation y = -x^2 + 8x - 12. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
To transform the given equation into the vertex form, we need to complete the square.
1. Start with the given equation: y = -x^2 + 8x - 12.
2. Rewrite the equation by grouping the x terms and leaving a space for completing the square: y = -(x^2 - 8x) - 12.
3. To complete the square, take half of the coefficient of x (which is -8), square it (which is 16), and add it inside the parentheses: y = -(x^2 - 8x + 16) - 12 - (-16).
4. Simplify the equation by combining like terms: y = -(x - 4)^2 + 4 - 12 + 16.
5. Further simplify to get the vertex form: y = -(x - 4)^2 + 8.
So, the vertex form of the equation is y = -(x - 4)^2 + 8.
Now, let's simplify the expression (-6i)².
When you square a complex number, you need to apply the rules for multiplying imaginary numbers.
1. Start with the expression (-6i)².
2. Square the real part and the imaginary part separately. In this case, (-6)² gives us 36 and (i)² gives us -1.
3. Multiply the two results. -1 multiplied by 36 is -36.
Therefore, (-6i)² simplifies to -36.
I hope this helps! Let me know if you have any further questions.