Final answer:
The equation of the quadratic function with a vertex of (1,1) and passes through (3,-7) is y = -2(x-1)^2 + 1.
Step-by-step explanation:
The quadratic function can be represented by the equation y = ax^2 + bx + c. To find the equation of the quadratic function with a vertex of (1,1) and passes through (3,-7), we can use the vertex form of a quadratic function, which is y = a(x-h)^2 + k, where (h, k) is the vertex. Plugging in the given vertex, we get y = a(x-1)^2 + 1.
To find the value of a, we substitute the coordinates of the point (3,-7) into the equation. We get -7 = a(3-1)^2 + 1, which simplifies to -7 = 4a + 1.
Quadratic functions are used in different fields of engineering and science to obtain values of different parameters. Graphically, they are represented by a parabola. Depending on the coefficient of the highest degree, the direction of the curve is decided. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic function is a “polynomial function of degree 2.” There are many scenarios where quadratic functions are used. Did you know that when a rocket is launched, its path is described by quadratic function?
In this article, we will explore the world of quadratic functions in math. You will get to learn about the graphs of quadratic functions, quadratic functions formulas, and other interesting facts about the topic. We will also solve examples based on the concept for a better understanding
Solving for a, we get a = -2. Substituting this value of a back into the equation, the equation of the quadratic function is y = -2(x-1)^2 + 1.