Find the parabola with equation y = ax2 + bx whose tangent line at (2, 8) has equation y = 12x − 16.

Step-by-step explanation:

Before we can calculate the equation of the parabola in the form

y = ax²+bx, we need to get the value of a and b.

First we need to set up a simultaneous equation as shown;

since y = ax²+bx

dy/de = y' = 2ax + b

Substitute the point (2, 8) into the equation

y' = 2a(2)+b

y' = 4a + b

Since y' is also the slope of the equation y = 12x-16, hence y' = 12 on comparison.

The equation becomes;

12 = 4a+b

4a+b = 12 1

Since the point (2, 8) is also on the parabola, then it must satisfy the equation y = ax²+bx

substitute the coordinate;

8 = a(2)²+b(2)

8 = 4a + 2b

4 = 2a + b

2a+b = 4 2

Solve equations  1 and 2 simultaneously

4a+b = 12 1

2a+b = 4 2

Substract both equation

4a - 2a = 12-4

2a = 8

a = 4

substitute a = 4 into equation 2 and get b;

From 2; 2a+b =4

2(4)+ b = 4

8+b = 4

b = 4-8

b = -4

Substitute a = 4 and b = -4 into the equation of the parabola y = ax²+bx

y = 4x²+(-4)x

y = 4x²-4x

y = 4x(x-1)

Hence the required equation of the parabola is y = 4x(x-1)

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

answer: what statements

step-by-step explanation if you write the statements down then i could you.