Question

Two quadratic functions are shown:

which function has lowest minimum value, and what are it's coordinates?​

function 1 has the lowest minimum value and it's coordinates are (-1,4)

function 1 has the lowest minimum value and it's coordinates are (0,7)

function 2 has the lowest minimum value and it's coordinates are (-1,7)

function 2 has the lowest minimum value and it's coordinates are (0,3)

Answer 1

To find the minimum value of function 1, we need to find the vertex. The formula for the x-coordinate of the vertex is -b/2a, which is -1 in this equation. However, to find minimum and maximum values, we need to look at the y-coordinate. f(-1) is 4, which we know is a minimum (rather than a maximum), because the leading coefficient is positive -- so the parabola opens upwards. So, the minimum value of f(x) is 4, and the coordinate is (-1, 4).

From the table, the minimum value of g(x) is 3, and the coordinate is (0, 3).

Therefore, function 2 has the lowest minimum value, with coordinates (0, 3).