find the vertex, axis of symmetry,y int and third point
3x^2-12x+10
Can someone give me a youtube link for this
-15x+12
The question probably was
y = 3x^2-12x+10
I will assume you are not taking Calculus, and will do it by completing the square.
y = 3(x^2-4x + 4 - 4) + 10
= 3((x-2)^2 - 4) + 10
= 3(x-2)^2 - 12 + 10
= 3(x-2)^2 - 2
vertex: (2,-2)
axis of symmetry : x = 2
y-intercept : 10
To find the vertex, axis of symmetry, y-intercept, and a third point of the quadratic equation given, we can use the equation in the form of y = ax^2 + bx + c, where a = 3, b = -12, and c = 10.
1. Vertex:
The x-coordinate of the vertex of the equation can be found using the formula x = -b / (2a). In this case, x = -(-12) / (2 * 3) = 12 / 6 = 2.
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation: y = 3(2)^2 - 12(2) + 10 = 12 - 24 + 10 = -2.
Therefore, the vertex of the equation is (2, -2).
2. Axis of Symmetry:
The axis of symmetry is a vertical line that passes through the vertex. In this case, the x-coordinate of the vertex is 2, so the equation for the axis of symmetry is x = 2.
3. Y-intercept:
To find the y-intercept, substitute x = 0 into the equation: y = 3(0)^2 - 12(0) + 10 = 0 - 0 + 10 = 10.
Thus, the y-intercept is (0, 10).
4. Third Point:
To find a third point, you can choose any value of x and substitute it into the equation to solve for y. Let's choose x = 4:
y = 3(4)^2 - 12(4) + 10 = 48 - 48 + 10 = 10.
So, the third point is (4, 10).
Apologies, but as an AI text-based assistant, I'm not able to provide links to external websites like YouTube. However, you can search on YouTube for quadratic equations or specifically the equation you have provided (3x^2 - 12x + 10) to find related videos.