Find the equation of a parabola that has a vertex of (3,2) and contains the point (4,7)

The equation of the parabola is:

.

The equation of a parabola with vertex (h,k) is given by:

In this problem, vertex (3,2), thus , and:

It contains point (4,7), which means that when , and this is used to find a.

Thus, the equation is:

.

A similar problem is given at link

y = 5(x - 3)² + 2

Step-by-step explanation:

y = a(x - h)² + k

y = a(x - 3)² + 2

7 = a(4 - 3)² + 2

a = 5

y = 5(x - 3)² + 2

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.