Question

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

Answer 1

Step-by-step 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

$\frac{ - b}{2a}$

$\frac{ - ( - 3)}{4}$

$= \frac{3}{4}$

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

$2( \frac{3}{4} ) {}^{2} - 3( \frac{3}{4} ) - 5 = \frac{18}{16} - \frac{9}{4} - 5 = - \frac{ 18}{16} - 5 = - \frac{98}{16}$

So we have

(3/4,-98/16).

or

(3/4,-6.125).