Quadratic Equations PDF

Unit 3: Quadratics Intro to Quadratics Homework: Unit 3 HW 1 What are Quadratics Equations? Parabolic Shape Can model gravity Speed of an object Find the best deals We use to to optimiz...

Unit 3: Quadratics Intro to Quadratics Homework: Unit 3 HW 1 What are Quadratics Equations? Parabolic Shape Can model gravity Speed of an object Find the best deals We use to to optimize profit Vocab Quadratic Equation: The highest exponent is 2. 𝑥2 Vertex: The highest or lowest point of your parabola. (Middle) Axis of Symmetry: The line that divides the parabola perfectly in two. Roots/Zeros/Solutions: These are the x-intercepts of the parabola. When y-value is at 0 Standard Form of a Quadratic Function Standard Form: y = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 a is the vertical stretch c is the y-intercept Maximums and Minimums MAX MIN ✓ Maximum is the highest point of ✓ Minimum is the lowest point of your parabola. your parabola. ✓ When the “a” value is negative ✓ When the “a” value is positive Class Practice 1. Part 1: Write each quadratic in standard form. Part 2: Determine if it will have a min or a max 𝑎. 𝑦 = 5𝑥 − 1 𝑥 + 3 𝑏. 𝑓 𝑥 = −3(𝑥 − 1)2 + 10 2. Given each quadratic equation below. Determine whether you have a min or max and how you know. a. 𝑓 𝑥 = −5𝑥 2 + 6𝑥 b. 𝑦 = −8𝑥 + 2𝑥 2 + 9 c. 17𝑥 − 3𝑥 2 = 𝑦 + 10 Standard Form: Formula for Vertex −𝒃 Formula for x-value of vertex: =𝒙 𝟐𝒂 −𝒃 Formula to y-value of vertex: 𝒇 =𝐲 𝟐𝒂 Your quadratic must be in standard form first for you to use this formula Class Practice 3. Find the vertex of each parabola, Write the axis of symmetry. Determine if the quadratics below has a minimum or a maximum: a. 𝑦 + 20𝑥 = −2𝑥 2 + 3 Aksel forgot to bring a pencil again. Sadie decided to loan him one of her. She tossed the pencil to him. The height of the pencil is modeled by h t = −𝑡 2 + 8𝑡 + 3.5 in feet after t seconds. a. What is the height of the candy before Sadie throws it? b. What is the height of the candy after 2.2 seconds after she throws it? 3. Find the vertex of each parabola, Write the axis of symmetry. Determine if the quadratics below has a minimum or a maximum: b. 𝑔(𝑥) = 6𝑥 + 𝑥 2 + 5 ALTERNATIVE RESOURCES Find more illustrations like these on Stories by Freepik