I think you mean you know how to put it in the form y = a(x - p)2 + q. Why not put it in this form and then expand the right hand side so it looks like y=ax2+bx+c?john_blah said:Homework Statement
Find the equation of the parabola if you have the following information:
Xintersects: (-4;0) and (0;0)
Yint: y = 7
Vertex: (-2;7)
Homework Equations
The equation must be in the standard form:
y=ax^2 + bx + c
The Attempt at a Solution
I know how to put it into the equation y = a(x^2 - p) + q but I have no idea how to put it into the y=ax^2 + bx + c form, which is asked.
Thanks
A parabola is a type of curve that is formed when a plane intersects with a cone at a particular angle. It is a U-shaped curve that can be seen in many real-life situations, such as the trajectory of a thrown ball or the shape of a satellite dish.
The equation of a parabola can be found using the general form: y = ax^2 + bx + c, where a, b, and c are constants. To find these values, you will need to know the coordinates of at least three points on the parabola or have information about the focus and directrix of the parabola.
The focus of a parabola is a fixed point on the curve that is equidistant from any point on the parabola and the directrix, which is a fixed line parallel to the axis of symmetry. These two elements are important in determining the shape and position of a parabola.
Yes, a parabola can have a negative coefficient for the x^2 term. This will result in a downward-facing parabola instead of the typical upward-facing parabola. The sign of the coefficient affects the direction in which the parabola opens.
Yes, there are different types of parabolas, such as standard, vertex, and intercept form. These different forms allow for easier graphing and interpretation of the parabola's features, such as its vertex, focus, and directrix.