Question

Consider the quadratic function f(x)=−x^2+4x+12

Determine the following:

The smallest xx-intercept is x=Incorrect
The largest xx-intercept is x=
The yy-intercept is y=

Answer 1

a) -2 from (-2,0) b) 6 from (6,0) c) y-intercept: 12 from (0,12)

Explanation:

The X intercepts in a quadratic function are the points of the x-axis crossed by the parabola. One quadratic equation may have up to two points on the X-axis. This or these points in the X-axis, the Zeros of this function, will be crossed by the parabola.

The Y-intercept is the point of the y-axis crossed by the parabola.

Solving the equation:

`-x^(2) +4x+12=0\\ x'=(-4+√(64))/(-2) \\ x`

S={-2, 6} These values, or zeros of this quadratic function are the X, intercepts.

c) The indepent term, or c, in f(x)= ax²+bx+c in this case is 12, also is the Y coordinate for the Parabola Vertex. This point is our intercept for y.