Question

Please help me with this question urgently! Thanks in advance.​

Answer 1

Explanation:

First. plug in values of x and try to form a curve. Since this a quadratic, we will get a parabola( a U shaped graph).

Plug in values from -3 to 4.

for x.

`f( - 3) = 2( - 3) {}^(2) - 3( - 3) - 5 = 22`

`f( - 2) = 2( - 2) {}^(2) - 3( - 2) - 5 = 9`

`f( - 1) = 2 + 3 - 5 = 0`

Keep going until you get until you get to 4 for x.

The graph above should be your curve.

1. The roots of a quadratic are the x values when y=0, here it is 2.5 and -1.

2. Since the leading degree coeffecient is positive, we have a minimum value. It hard to tell the minimum here so let put this in vertex form, we have

`2{x}^(2) - 3x - 5`

First. we do

`( - b)/(2a)`

`( - ( - 3))/(4)`

`= (3)/(4)`

Now, we plug that in to find our y intercept of the minimum.

`2( (3)/(4) ) {}^(2) - 3( (3)/(4) ) - 5 = (18)/(16) - (9)/(4) - 5 = - ( 18)/(16) - 5 = - (98)/(16)`

So we have

(3/4,-98/16).

or

(3/4,-6.125).