Question

Sketch the quadratic function f(x) = -2x2 + 4x + 6. Which key feature of the graph is not true?

Answer 1

Answer:

D is false

Step-by-step explanation:

f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:

f(x) = -2x^2 + 4x + 6.

Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex.  We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.

Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8.  So statement A is true:  there's a max at (1, 8).  This is also the vertex of the graph.

Let's now look at C and D.  We evaluate f(x) at x = 3 and x - 2.  If the output (y) value is 0, we know we have an x - intercept:

f(3) = -2(9) + 4(3) + 6 = 0.  Yes, C is true, (3, 0) is an x-intercept.

f(-2) = -2(4) - 8 + 6 is not 0.  Therefore D is false; (-2, 0) is not an x-intercept.

Look at B:  Let x = 0 and find y:  it's 6.  Thus, (0, 6) is the y-intercept.  B is true.