How can I find the vertex, axis of symmetry? I know to find x and y intercepts i use the quadratic formula.
I am given the parabola y=x^2+6x+5
I do not want the answer.. Just please explain to me how to solve for it. what method do I use???
y coordinates of the vertex = f ( x ) = f ( x = - b / 2a ) = c - b ^ 2 / 4a
To find the vertex and axis of symmetry of a parabola, you can use the formula -b/2a. In your case, you have the equation y = x^2 + 6x + 5.
First, let's identify the coefficients a, b, and c. In this case, a = 1, b = 6, and c = 5.
To find the x-coordinate of the vertex, you can use the formula -b/2a. Plug in the values:
x-coordinate of vertex = -(6)/(2*1) = -6/2 = -3.
Now, substitute this x-value back into the original equation to find the y-coordinate of the vertex.
y = (-3)^2 + 6(-3) + 5 = 9 - 18 + 5 = -4.
Therefore, the vertex of the parabola is (-3, -4).
The axis of symmetry is a vertical line that passes through the vertex. In this case, the equation of the axis of symmetry is x = -3.
Remember, this method applies to parabolas in the form y = ax^2 + bx + c, where a, b, and c are constants.
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.
This point, where the parabola changes direction, is called the "vertex".
To determine the vertex of the graph of a quadratic function:
f(x) = a x ^ 2+ b x + c
we can either:
1) Use the method of completing the square to rewrite the function in the form:
f(x) = a ( x - h ) ^ 2 + k
The vertex poit is a point with coordinates: (h, k)
x coordinates of the vertex = h
y coordinates of the vertex = k
OR
2) Use the formula:
x coordinates of the vertex = - b / 2a
y coordinates of the vertex = f ( x ) = c - b ^ 2 / 4a
The axis of symmetry is a vertical line through the vertex.
The equation of the axis of symmetry is the equation of the vertical line passing through x and y coordinate of the vertex:
The equation of the axis of symmetry:
x = x coordinate of the vertex
For each value of y
x = - b / 2a