Question

Consider the quadratic function f, given by f(x) = −x2 + 6x−8. (i) Determine if the graph of y = −x2 + 6x − 8 is concave up or concave down, providing a justification with your answer. (ii) Re-write the equation of the quadratic function f, given by f(x) = −x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the square. Hence determine the vertex of the graph of y = f(x).

(iii) Identify the x-intercepts and y-intercept of the graph of y = f(x). (iv) Sketch a graph of y = −x2 + 6x−8 clearly labelling the vertex of the parabola, along with any intercepts with the x- and y-axes

Answer 1

(i) Graph is below:

This is concave down.

(ii)

Vertex is at

(iii) X intercepts are at

So are the X-intercepts

Y intercepts are

Only Y-intercept is

(iv) Graph with everything labelled: