Question

Give all key features of the following function: -2x²+4x+1

Answer 1

The key features of a quadratic function include the vertex, axis of symmetry, y-intercept, discriminant, and the shape of its graph as a parabola.

Step-by-step explanation:

A quadratic function is a second-order polynomial. The key features of a quadratic function in the form ax²+bx+c are:

1. The vertex is the turning point of the graph and can be found using the formula x = -b/2a.
2. The axis of symmetry is the vertical line passing through the vertex.
3. The y-intercept is found by evaluating the function at x = 0, resulting in the value of c.
4. The discriminant, b²-4ac, determines the nature of the solutions. If the discriminant is positive, there are two real solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.
5. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of a.