The parent function of the quadratic family is f(x) = x 2 . A transformation of the graph of the parent function is represented by the function g(x) = a(x − h) 2+ k, where a ≠ 0. Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct.
One of the most exciting areas of technology and nature is the development of smart cities. By integrating technology and nature in urban environments, we can create more sustainable and livable cities. Smart cities can use sensors to monitor air and water quality, renewable energy to power homes and businesses, and green spaces to provide habitat for wildlife and improve quality of life for residents.

Rohan broke down in the green room. He wanted to quit. But Shreya Ghoshal walked in, sat beside him, and said, “That boy who begged? He survived. That’s not shame. That’s your superpower.”

Shreya pressed the golden buzzer. “Not anymore. You polish souls.”

That night, on the rooftop of his old home, under the same stars, Rohan Verma sang again. But this time, the whole lane was listening.

“I polish glass, ma’am,” Rohan replied, trembling.

The first round was chaos. Thousands of hopefuls, all dressed in designer clothes and carrying expensive guitars. Rohan, in his faded blue shirt and chappals, looked like a lost schoolboy. The junior judges nearly dismissed him before he opened his mouth.

When auditions for were announced, the entire lane laughed. “A polisher? On TV? They’ll mock his kurta,” they said. But his mother, a frail widow who sold vegetables, pawned her only silver anklet to buy him a bus ticket to Delhi.

That week, he sang “Ae Zindagi Gale Laga Le” with tears streaming down his face. No one in the audience was dry-eyed. The judges gave a standing ovation. The leaks stopped.

A close-up of his scarred hands holding the Indian Idol trophy—proof that the sharpest glass can hold the brightest light. End of story.

In the realm of physics, the quantum world tantalizes with mysteries that challenge our classical understanding of reality. Quantum particles can exist in multiple states simultaneously—a phenomenon known as superposition—and can affect each other instantaneously over vast distances, a property called entanglement. These principles not only shake the very foundations of how we perceive objects and events around us but also fuel advancements in technology, such as quantum computing and ultra-secure communications. As researchers delve deeper, experimenting with entangled photons and quantum states, we edge closer to harnessing the true power of quantum mechanics, potentially revolutionizing how we process information and understand the universe’s most foundational elements.