Question

F(x) = 2x^2 − 3x − 5 Part

Answer 1

Answer:  Answer  is in the steps..

Step-by-step explanation:

f(x)= $2x^{2}$ - 3x -5        

A) To find the x intercepts of a parabola we have to set the whole equation equal zero because the x intercept is when y equal zero in other words where f(x) equal zero.

 $2x^{2}$  - 3x - 5 = 0     Now solve using quadratic formula.

  x = -b±$\frac{\sqrt{b^2 -4ac } }{2a}$    

  x = 3 ± $\sqrt{9+40} /2a$  

   x = 3 ± $\sqrt{49}$  / 2a

   x= 3 ± 7 /4

   x= -1   or x = 5/2  

The x intercepts are  (5/2,0)  and (-1,0)

   

B)  The graph vertex of the graph of f(x)  is going to be at a minimum because the leading coefficient of the function has a positive integer which means the parabola will open up and its vertex will be at the minimum point.

 Using the  x coordinates  we could find their average and find the x coordinate of the   vertex.

$\frac{5}{2} + -\frac{1}{1}$  =  $\frac{3}{2} / \frac{2}{1}$ = 3/4  

The x coordinate of the vertex  is 3/4 so we will input that into the equation and solve for the y coordinate  

$2(\frac{3}{4})^2 - 3 (\frac{3}{4}) - 5$   = 18/16 - 9/4 -5  =  -49/8

The y coordinate of the vertex  is  -49/8

So the vertex is (3/4, -49/8)  

C)   First  I will graph the vertex and then graph he two x intercepts and connect then like a U shape.