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Quadratic Functions and Their Graphs A quadratic function is a polynomial function of degree 2, typically written in the form: $$f(x) = ax^2 + bx + c$$ where a, b, and c are constants and a ≠ 0. Important Properties of Quadratic Function Graphs Y-Intercept: The point where the parabola crosses the y-axis (0, c) X-Intercepts: Also known as zeros, roots, or solutions - points where the parabola crosses the x-axis Vertex: The highest or lowest point of the parabola Axis of Symmetry: A vertical line that passes through the vertex, dividing the parabola into two symmetrical halves Forms of Quadratic Functions 1. Standard Form $$f(x) = ax^2 + bx + c$$ To find the axis of symmetry: $$x = -\frac{b}{2a}$$ 2. Vertex Form $$f(x) = a(x - h)^2 + k$$ Where (h, k) is the vertex of the parabola Characteristics of Parabolas If a > 0, the parabola opens upward (U-shaped) If a < 0, the parabola opens downward (∩-shaped) The larger the

Review Chapter 2-4 Chapter 2 Given that y is an integer, -3 < y ≤ 2.7, and y ≠ 0, write down all the possible values of y . It is given that z ≥ 41.5. Write down the least possible value of z if z is: an integer a prime number a perfect square Suggest a possible value of z for which z is a factor of 1260 and z is an even number. Solve the inequality 7 - (1/3) x ≥ 5 and represent the solution on a number line. A smartphone costs $750. Form an inequality and solve it to find the maximum number of smartphones that a company can buy with a budget of $25,000. Consecutive Even Numbers: Let the numbers be z , z +2, z +4. If the inequality z +( z +2)+( z +4)>120 is given, find the smallest even number z that satisfies this condition and calculate the product of t

Understanding Kinetic, Potential, and Mechanical Energy: A Comprehensive Guide Understanding Kinetic, Potential, and Mechanical Energy: A Comprehensive Guide Energy is a fundamental concept in physics, playing a crucial role in understanding how objects move and interact. In this comprehensive guide, we'll explore three important types of energy: kinetic energy, potential energy, and mechanical energy. We'll dive into their definitions, formulas, and real-world applications, complete with illustrative examples and practice problems. 1. Kinetic Energy Kinetic energy is the energy possessed by an object due to its motion. It depends on both the object's mass and its velocity. Formula: KE = ½ mv² Where: KE = Kinetic Energy (measured in Joules, J) m = mass of the object (in kilograms, kg) v = velocity of the object (in meters per second, m/s)

Mastering Quadratic Functions: A Comprehensive Guide to Graphs and Properties Mastering Quadratic Functions: A Comprehensive Guide to Graphs and Properties Welcome to our in-depth exploration of quadratic functions and their graphs! Whether you're a student looking to ace your next math test or an enthusiast wanting to deepen your understanding, this guide will walk you through the essential concepts, properties, and applications of quadratic functions. 1. Introduction to Quadratic Functions A quadratic function is a polynomial function of degree 2, typically written in the form: f(x) = ax² + bx + c Where 'a', 'b', and 'c' are constants, and 'a' ≠ 0. The graph of a quadratic function is called a parabola, which has a distinctive U-shape (or inverted U-shape if 'a' is negative).

Factoring Quadratic Equations Factoring quadratic equations is a method to express a quadratic expression in the form $$ax^2 + bx + c$$ as a product of its linear factors $$(x - r_1)(x - r_2)$$, where $$r_1$$ and $$r_2$$ are the roots of the equation. Steps for Factoring Quadratic Equations: Identify the coefficients $$a$$, $$b$$, and $$c$$ in the quadratic equation $$ax^2 + bx + c = 0$$. Find two numbers $$p$$ and $$q$$ such that: $$p + q = b$$ $$pq = ac$$ Rewrite the middle term using $$p$$ and $$q$$: $$ax^2 + px + qx + c$$ Group the terms and factor out common factors: $$ax^2 + px + qx + c = (ax^2 + px) + (qx + c) = x(ax + p) + 1(qx + c)$$ Factor out the greatest common factor: $$(x(ax + p) + 1(qx + c)) = (x + \frac{c}{q})(ax + p)$$ Example: Factor the quadratic equation: $$x^2 + 7x + 12 = 0$$ Solution: Identify $$a=1$$, $$b=7$$, and $$c=12$$ Find $$p$$ and $$q$$: $$3 + 4 = 7$$ and $$3 \times 4 = 12$$ Rewrite: $$x^2 + 3x + 4x + 12$$ Group and factor: $$(x^2 + 3

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1:   Fullscreen Mode   Acceleration Formula:

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

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Halo, sobat blogger. Apa kabar? Semoga sehat dan bahagia selalu. Kali ini, saya akan berbagi tentang latihan UTS Sistem Pencernaan & zat adiktif Pada Makanan. Materi ini sangat penting untuk kalian yang sedang belajar Biologi kelas 8 SMP. Sistem pencernaan adalah sistem yang berperan dalam mencerna, menyerap, dan mengeluarkan makanan yang kita konsumsi. Namun, tidak semua makanan baik untuk sistem pencernaan kita. Ada beberapa makanan yang mengandung zat-zat adiktif yang bisa merusak organ pencernaan, menyebabkan gangguan kesehatan, atau bahkan membuat kita ketagihan. Zat-zat adiktif ini antara lain gula, garam, kafein, nikotin, alkohol, dan narkoba. Nah, bagaimana cara mengenali zat-zat adiktif ini? Bagaimana dampaknya bagi tubuh kita? Bagaimana cara menjaga sistem pencernaan kita tetap sehat dan bugar? Oke, tanpa berlama-lama lagi, mari kita mulai latihan  tentang sistem pencernaan dan zat-zat adiktif pada makanan. Selamat latihan dan semoga bermanfaat.

Halo, selamat datang di blog saya. Di sini, saya akan berbagi tentang contoh soal latihan SPLDV (sistem persamaan linier dua variabel) yang bisa kamu kerjakan untuk mengasah kemampuanmu dalam menyelesaikan masalah matematika. SPLDV adalah suatu sistem yang terdiri dari dua atau lebih persamaan linier yang memiliki dua variabel, misalnya x dan y. SPLDV sering digunakan untuk menyelesaikan masalah-masalah matematika yang berkaitan dengan harga, keuntungan, ukuran, dan sebagainya. Ada beberapa metode yang bisa kita gunakan untuk menyelesaikan SPLDV, yaitu metode grafik, metode substitusi, metode eliminasi, dan metode gabungan. Pada blog ini, saya akan memberikan beberapa contoh soal SPLDV beserta penyelesaiannya dengan menggunakan metode substitusi. Semoga bermanfaat dan selamat belajar! 😊 No. 1-5. Tentukan himpunan penyelesaian setiap SPLDV berikut! 1. 𝑦 = 2𝑧 𝑑𝑎𝑛 𝑦 + 3𝑧 = 20 2. 𝑦 + 4 = 6 𝑑𝑎𝑛 3𝑦 − 𝑧 = 7 3. 2𝑦 + 𝑧 = 14 𝑑𝑎𝑛 3𝑦 − 2𝑧 = 42 4. 2𝑦 − 3𝑧 = 11 𝑑𝑎𝑛 − 3