In Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options.

Key Concepts

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'. Understanding the general shape and properties of parabolas is essential for analyzing their equations.

Vertex Form of a Quadratic

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. This form is particularly useful for identifying the vertex directly from the equation and for graphing the function. In the provided graph, the vertex is at (-1, 7), which indicates the highest point of the parabola since it opens downwards.

Y-Intercept

The y-intercept of a function is the point where the graph intersects the y-axis, which occurs when x = 0. For quadratic functions, the y-intercept can be found by evaluating the function at x = 0. In the given graph, the y-intercept is at (0, 8), which helps in determining the specific equation of the quadratic function by providing another point through which the parabola passes.