Use the discriminant to determine all values of k which would result in the graph of the equation y = -2x2 + kx – 18 being tangent to the x-axis.

k = ±12

Step-by-step explanation:

Equation of the graph is,

y = -2x² + kx - 18

Discriminant of a quadratic equation, y = ax² + bx + c is defined by

Discriminant = √(b²- 4ac)

If √(b²- 4ac) = 0,

Equation will have one real solution.

Discriminant of the the given equation = √[k² - 4(-2)(-18)]

Since, graph of the equation is tangent to the x-axis, there will be one real solution.

Therefore, √[k² - 4(-2)(-18)] = 0

k² - 144 = 0

k = ±√144

k = ±12

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

if x = 1, then the answer is 3.5