You can check for yourself. If x = -2, is y = 5? Does it go through the origin?rowdy3 said:Find the equation of the parabola (in standard form) whose vertex is at the origin, has a vertical axis, and passes through the point (-2,5). Thanks
y = ax^2
sub in the point (-2, 5) and solve for a
5 = a(-2)^2
5 = a(4)
a = 5/4
Final equation is y = (5/4)x^2. Is that right?
A parabola is a type of curve that is created by the graph of a quadratic function, y = ax^2 + bx + c. This equation is known as the standard form of a parabola.
The main features of a parabola are its vertex, axis of symmetry, and focus. The vertex is the highest or lowest point on the parabola, depending on whether it is opening upwards or downwards. The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two equal halves. The focus is a fixed point on the axis of symmetry that helps determine the shape of the parabola.
To find the equation of a parabola, you need to have three points on the curve. These points can be used to create a system of equations, which can then be solved to find the coefficients a, b, and c in the standard form equation. Once these values are known, you can write the equation of the parabola in the form y = ax^2 + bx + c.
The main difference between a parabola that opens upwards and one that opens downwards is the sign of the coefficient a in the standard form equation. If a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards. This affects the location of the vertex and the direction that the curve opens.
No, a parabola cannot have a horizontal axis of symmetry. The axis of symmetry is always a vertical line passing through the vertex of the parabola. This is because the equation of a parabola is symmetric about its axis, meaning that any point on one side of the axis will have a corresponding point on the other side of the axis with the same y-value.