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3 years ago

Find the vertex, the axis of symmetry, and the y-intercept of the graph.

Mathematics

1 answer:

UNO [17]3 years ago

6 0

Given:

Given that the graph of the parabola.

We need to determine the vertex, the axis of symmetry and the y - intercept of the graph.

Vertex:

The vertex of the parabola is the point at which the parabola changes its direction.

From the graph, it is obvious that the parabola changes its direction at the point (-2,0)

Hence, the vertex of the graph is (-2,0)

Axis of symmetry:

The axis of symmetry is the line that divides the parabola exactly into two equal halves.

Hence, from the graph, it is obvious the line x = -2 divides the graph exactly into two equal halves.

Hence, the axis of symmetry is x = -2.

y - intercept:

The y - intercept of the parabola is the value of y when x = 0.

In other words, the y - intercept of the graph is the value of y when the line passes through the y - axis.

Thus, from the graph it is obvious that when x = 0, the value of y is -3.

Hence, the y - intercept of the graph is -3.

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2 years ago

Installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. If the

VikaD [51]

Answer:

(a). $1465.42

(b). $214.58

Step-by-step explanation:

We have been given that installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. The interest rate is 1.25% per month on the unpaid balance.

(a) To find the cost of the TV, we will use monthly payment formula.

$R=\frac{Pi}{1-(1+i)^{-n}}$ , where,

R = Periodic payment,

P = Loan amount,

i = Monthly interest rate in decimal form,

n = Number of total payments.

$n=3\times 12=36$

$1.25\%=\frac{1.25}{100}=0.0125$

$30=\frac{P*0.0125}{1-(1+0.0125)^{-36}}$

$30=\frac{0.0125P}{1-(1.0125)^{-36}}$

$30=\frac{0.0125P}{1-0.6394091578134724264}$

$30=\frac{0.0125P}{0.3605908421865275736}$

$10.817725265595827208=0.0125P$

$0.0125P=10.817725265595827208$

$P=\frac{10.817725265595827208}{0.0125}$

$P=865.41802124766617664$

$P\approx 865.42$

We know that total cost of TV would be equal to down payment plus amount of loan that is:

$865.42+600=1465.42$

Therefore, the total cost of the TV would be $1465.42.

(b). First of all, we need to find total amount paid in 3 years by multiplying amount of each monthly payment by 36 (3 years equal to 36 months).

$\$30\times 36=\$1080$

To find the total amount of interest paid, we will subtract amount of loan from total payment.

$\$1080-\$865.42=\$214.58$

Therefore, the total amount paid in interest would be $214.58.

8 0

3 years ago