Answer:
Answers explained below.Step-by-step explanation:
Part A.
For x-intercepts,
2x² - 3x - 5 = 0
2x² + 2x - 5x - 5 = 0
2x(x + 1) - 5(x + 1) = 0
(2x - 5)(x + 1) = 0
2x - 5 = 0 and x + 1 = 0
x = 2.5 and x = -1
Part B.
As the coefficient of the x² term is positive, the parabola open up, and the vertex is a minimum. The coordinates of the parabola are given by -[b/2a, f(-b/2a)] where a and b represent the coefficients of a parabola in the standard form ax² + bx +c = 0.
In this case a = 2, b = -3, c = -5.
So -b/2a = -(-3)/(2 × 2)
= 3/4 and
f(-b/2a) = 2(3/4)² - 3(3/4) - 5
= 2(9/16) - 9/4 - 5
= -6.125
The coordinates of the vertex are (0.75, -6.125)
Part C.
To graph this function,
Firstly, establish where the vertex will be from the coordinates found.
Next, plot the position of the x intercepts. You know it opens up, so you would draw it so the vertex is a minimum.
You could also get the y intercept by letting x = 0, which gives -5 for the y intercept. This should give you a rough idea of what the graph looks like.