its graph opens upward and its vertex is at the origin. give an example of a quadratic function.
y = x^2
or y = 2 x^2
or y = 3 x^2
or y = pi x^2
or y = 5139.564 x^2 :)
To find an example of a quadratic function with a graph that opens upward and has the vertex at the origin, we can use the standard form of a quadratic function, which is:
f(x) = ax^2 + bx + c
Given that the vertex is at the origin (0, 0), we know that the x-coordinate of the vertex is 0. Substituting this into the quadratic equation, we get:
f(0) = a(0)^2 + b(0) + c
0 = c
So, we know that c equals 0. Now, let's consider the statement that the graph opens upward. For a quadratic function to open upward, the coefficient 'a' needs to be positive.
Putting it all together, an example of a quadratic function that satisfies these conditions is:
f(x) = ax^2 + bx
where 'a' is a positive real number, and 'b' can take any real value.