Answer:
Explanation:
the coefficients of this quadratic are -1, 4 and 4, and so the discriminant b^2 - 4ac works out to 16 - 4(-1)(4), or 0. Thus this graph has two real, equal roots which are the same point on the graph, the vertex, the maximum of the function.
Letting x = 0, we find that y is 4. Thus, the y-intercept is (0, 4). Plot this.
Using the formula x = -b / [2a], we find the axis of symmetry:
x = -4 / [2*(-1)] = -4 / [-2] = +2
The axis of symmetry is the vertical line x = 2.
At x = 2, y = -(2)^2 + 4(2) + 4, OR -4 + 8 + 4, or 0.
The vertex and maximum value are (2, 0). The graph touches the x-axis in only one place.
Draw the axis of symmetry x = 2. Plot the vertex (2, 0) and the y-intercept. Reflect the y-intercept about the axis of symmetry to obtain a second point on the graph at the same y-value as (0, 4).