hi guys need help with a few questions.
1. Which equation represents the axis of symmetry of the function y = 2x^2+4x-6? A. y= 1 B. x= 1 C. x=3 D x= -3
2. & 3. What are the coordinates of the vertex of the graph of the function -
2. y = -x^2+6x-11 A. (3,-2) B. (3,16) C. (-3,-29) D. (-3,-20)
3. y = -3x^2 -12x + 3 A. (-2,29) B (2,-15) C. (2, -9) D. (-2,15)
Okay I’m just gonna do what everyone wants and what I came here to find but couldn’t
Here’s the answers
1.B
2.A
3.D
4.B
5.D
6.B
I got almost nothing on my quick check so that I could see the correct answers and give them to you guys
This is what the quick check says were actually the correct answers do have fun
recall that for y = ax^2+bx+c the axis and vertex always lie on the line
x = -b/2a
@steve what question r u talking about
Sure! I can help you with these questions.
1. To find the axis of symmetry of a quadratic function in the form y = ax^2 + bx + c, you need to use the formula x = -b/2a. In this case, the given function is y = 2x^2 + 4x - 6. So the equation representing the axis of symmetry is x = -4/(2*2). Simplifying that, you get x = -1. So, the correct answer is B. x = 1.
2. To find the coordinates of the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b/2a to find the x-coordinate of the vertex. Then substitute this value back into the equation to find the y-coordinate.
For the function y = -x^2 + 6x - 11, the x-coordinate of the vertex can be found using x = -b/2a. Inserting the values from the equation, you get x = -6/(2*(-1)) = -6/(-2) = 3. Substituting this value into the equation, y = -(3)^2 + 6(3) - 11, simplifying you get y = -9 + 18 - 11 = -2. So, the coordinates of the vertex are (3, -2). The correct answer is A. (3, -2).
3. Similar to the previous question, for the function y = -3x^2 - 12x + 3, the x-coordinate of the vertex can be found using x = -b/2a. Inserting the values from the equation, you get x = -(-12)/(2*(-3)) = -12/(-6) = 2. Substituting this value into the equation, y = -3(2)^2 - 12(2) + 3, simplifying you get y = -12 - 24 + 3 = -33. So, the coordinates of the vertex are (2, -33). The correct answer is not listed among the options provided, so none of the options is correct.
Steve's "big hint" applies to all 3 of your questions.
I will use it on #3
comparing:
y = ax^2 + bx + c , and
y = -3x^2 - 12x + 3, ---> a=-3, b=-12, c=3
the x of the vertex is -b/(2a) = -(-12)/-6 = -2
which also means that the axis of symmetry is
x = -2
to get the y of the vertex, plug it in
y = -3(-2)^2 - 12(-2) + 3
= -3(4) + 24 + 3 = 15
So the vertex is (-2,15)
Now, you do the other two.