Solve for x and round your answer to the nearest tenth.

determine the quadratic function of f whose graph is given. The vertex is (1,-3) and the y-intercept is -2

LuckyWell [14K]

Hmmm the y-intercept is at -2? what does that mean? well, is where the graph "intercepts" or touches the y-axis, and when that happens, x = 0, so the point is really ( 0 , -2 ).

and we know where the vertex is at. Let's assume a vertical parabola, in which case the squared variable is the "x".

$\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\
x=a(y-{{ k}})^2+{{ h}}
\end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\
vertex
\begin{cases}
h=1\\
k=-3
\end{cases}\implies y=a(x-1)^2-3
\\\\\\
\textit{now, we also know that }
\begin{cases}
x=0\\
y=-2
\end{cases}\implies -2=a(0-1)^2-3
\\\\\\
1=a(-1)^2\implies \boxed{1=a}\qquad thus\implies 
\begin{cases}
y=1(x-1)^2-3\\
\textit{or just}\\
y=(x-1)^2-3
\end{cases}$

6 0

3 years ago

A plane takes off and climbs steadily for 15 minutes until it

Nezavi [6.7K]

Step-by-step explanation:

Mark each mark by 15 mins add an extra tick at the time section

the corner before the first 15 min mark make a tilted line to 15 mins and 30,000 feet draw a straight line till 2 hours and 15 mins draw titled down to 2 hours and 30 mins

4 0

2 years ago

Multiply c by 9, then add 2 to the result

Novosadov [1.4K]

Answer:

9c+2

Step-by-step explanation:

6 0

2 years ago

Help me please solve the circled question show your work

Rasek [7]

Part 1) Use the fact that there are 12 inches in a foot

a) How many inches tall is a 7 foot basketball player?

we know that

1 foot=12 inches

so by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{7} \frac{inches}{feet} \\ \\x=12*7\\ \\x=84\ inches$

therefore

the answer Part 1a) is

$84\ inches$

Part b) If a yard is a 3 feet long, how many inches are in a yard?

we know that

1 yard=3 feet

1 foot=12 inches

so

Convert 3 feet to inches

by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{3} \frac{inches}{feet} \\ \\x=12*3\\ \\x=36\ inches$

therefore

the answer Part 1b) is

$36\ inches$

Part 2) At the farmer's market two pounds of peaches cost $4.20 How much will five pounds cost?

by proportion

$\frac{4.20}{2} \frac{\$}{pounds} =\frac{x}{5} \frac{\$}{pounds} \\ \\2*x=4.2*5\\ \\x=4.2*5/2=\$10.5$

therefore

the answer Part 2) is

$\$10.5$

Part 3) Janice mother gave her a ten dollars bill to buy five pounds each of bananas and apples at the grocery store. When she got there she found that bananas were 80 c per pound and apples were $1.40 per pound.

Did Janice's mother give her enough money? If so, should she receive any change? If not, how much more money does she need?

we know that

Find the cost of the bananas

$5\ pounds*0.80\frac{\$}{pounds}=\$4$