Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 1: Exercise

If the McDonald's logo is constructed as $2$ parabolic curves of the form $y=-M{\left(x-6\right)}^2 \text{and }y=-M{\left(x+6\right)}^2$. If the McDonald's logo has a height to length ratio of $1.5$, then find the value of $M$.

The main span of the Howrah bridge in Kolkata, West Bengal is about $194 \mathrm{m}$ long. The height of the towers is $26.2 \mathrm{m}$. The supporting cable for the main span of the bridge touches the road deck at the centre of the span. The parabola shown in the graph models the supporting cable of the main span of the Howrah Bridge and the green line segment represents the towers. Write down the values of $m, n, p$.

The diagram shows the graph of the function $y=A{x}^2+Bx+C$.

Complete the table below to show whether each expression is positive, negative or zero.

$\begin{array}{|llll|}\hline \text{ Expression }& \text{ positive }& \text{ negative }& \text{ zero }\\ A& & & \\ C& & & \\ B^2-4AC& & & \\ B& & & \\ \hline\end{array}$

Consider a person throwing a basketball $10 \text{m}$ above the ground. The basketball will reach its peak height and fall back to the ground. At time $t$, the height $h$ from the ground is given by $h=-2t^2+8t+10$. Calculate the time taken by the basketball to reach the ground.

A hotel famous for barfi makes barfi in the shape of a right angle triangle. Rahul who is fond of eating barfis goes to the hotel and orders$10$ barfi for himself and his friends. When the barfi were served, they found that the Perimeter of each barfi was $60 \mathrm{cm}$, while the hypotenuse was $25 \mathrm{cm}$. With this information, they all calculated the area of the barfi and each had different answers. The correct area of the barfi is $?$

When buying Embibe T-shirts, Raju determines that the total cost of buying $X$ T-shirts is given by the function,

$F\left(X\right)=0.04X^2-36X+9000$

If he wants to minimize the total cost of buying the T-shirts, how many shirts should he buy?

Alia and Ranbir went to Varanasi during their holidays. Alia wanted to visit all the ghats of Varanasi. So, they hired a motor boat for this purpose. While riding, Ranbir observed that the speed of motor boat was $20 \mathrm{km}/\mathrm{h}$. He was curious to know the speed of river Ganga. So, he noted the time taken by the boat to travel upstream and downstream in the river. He noticed that the boat took $1$ hour more to travel upstream than downstream to cover a distance of $15 \mathrm{km}$. Find the speed of the river Ganga in $\mathrm{km}/\mathrm{h}$.

If the curve $y=x^2+bx+c$ touches the $x-$axis at some point and intersects the $y-$axis at $\left(0, 9\right)$, find the absolute value of $b$.