What are the coordinates of the vertex of the graph of the function y = –3x² –12x + 3?
A.(–2, 29)
B.(2, –15)
C.(2, –9)
D.(–2, 15)
I think it is D?
A parabola which opens up has a lowest point and a parabola which opens down has a highest point.
The highest or lowest point on a parabola is called the vertex.
The parabola is symmetric about a vertical line through its vertex, called the axis of symmetry.
x - coordinate of vertex
x = - b / 2 a
In this case:
x = - ( - 12 ) / [ 2 ( - 3 ) ] = 12 / - 6 = - 2
y - coordinate:
y = - 3 ( - 2 ) ^ 2 - 12 ( - 2 ) + 3 =
- 3 * 4 + 24 + 3 = - 12 + 24 + 3 = 15
Answer D
Thank you very much
Well, solving for the vertex of the graph of the function y = –3x² –12x + 3, we can use the formula for the x-coordinate of the vertex, which is x = -b/(2a). In this case, a = -3 and b = -12. Plugging in these values, we get x = -(-12)/(2(-3)) = 12/-6 = -2. Now, to find the y-coordinate, we substitute x = -2 into the equation: y = –3(-2)² –12(-2) + 3 = -12 + 24 + 3 = 15. Therefore, the coordinates of the vertex are (-2, 15). So, the correct answer is D.(–2, 15). But hey, if clowns were in charge of math, we might have coordinates like (2, -9) just to keep things interesting!
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. Once you have the x-coordinate, you can substitute it into the function to find the corresponding y-coordinate.
In this case, the function is y = -3x^2 - 12x + 3. To find the x-coordinate of the vertex, we can use the formula x = -b/2a. In this case, a = -3 and b = -12. Plugging these values into the formula, we have:
x = -(-12)/2(-3)
x = 12/(-6)
x = -2
So, the x-coordinate of the vertex is -2.
Next, we substitute this x-coordinate into the function to find the y-coordinate:
y = -3(-2)^2 - 12(-2) + 3
y = -3(4) + 24 + 3
y = -12 + 24 + 3
y = 15
Therefore, the vertex of the graph of the function y = -3x^2 - 12x + 3 is (–2, 15).
So, the correct answer is option D, (–2, 15).
To find the coordinates of the vertex of the graph of the function y = –3x² –12x + 3, we can use the formula for the x-coordinate of the vertex, which is given by -b/2a.
In this case, the coefficient of x² is -3, and the coefficient of x is -12. Thus, the x-coordinate of the vertex is given by -(-12)/(2*(-3)) = 12/(-6) = -2.
Now, to find the y-coordinate of the vertex, we substitute the x-coordinate (-2) back into the original equation. Thus, y = -3*(-2)² - 12*(-2) + 3 = -12 - (-24) + 3 = 15 + 3 = 18.
So the coordinates of the vertex are (-2, 18).
Therefore, the correct answer is D. (–2, 15) is incorrect. The correct answer is (–2, 18).