Answer:
Below in bold.
Step-by-step explanation:
Part A
At the x-intercepts f(x) = 0, therefore:
2x^2 - 3x - 5 = 0
(2x - 5)(x + 1) = 0
x = 5/2, -1)
So the x intercepts are (-1, 0) and (5/2, 0).
Part B
The Coefficient of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.
Convert f(x) to vertex form, by completing the square:
f(x) = 2x^2 - 3x - 5
= 2(x^2 - 3/2x) - 5
= 2[(x - 3/4)^2 - 9/16] - 5
= 2(x - 3/4)^2 -18/16 - 80/16
= 2(x - 3/4)^2 - 49/8
So the coordinates of the vertex are
(3/4, -49/8) or
(0.75, -6.125) in decimal form.
Part C
To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.
The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).
You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.
Suggest x = - 2 and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 = 11.
- that is the point (-2,11) and the other would be x = 4, f(x) = 15. (4, 15)
Once you have plotted these points draw a smooth u shaped curve through them.
