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This topic introduces quadratic functions, their graphs and their important characteristics. Quadratic functions are widely used in mathematics and statistics. They are found in applied and theoretical mathematics, and are used to model non-linear relationships between variables in statistics.
Essential Questions. 1. What is the shape of the quadratic function and how can we use its features productively? 2. How can we find the zeros of a quadratic function? 3. How do we calculate the max or min of a quadratic function? 5.1 Rectangular fences. Question 5.1. You want to make a rectangular pen for Ellie, your pet elephant. What?!
For example, fireworks, when fired, follow a parabolic path and many explode when the vertex is reached. This unit will introduce you to quadratic functions. In addition, you will solve quadratic equations using factoring and the Zero Product Property.
Quadratic Equations. mc-TY-quadeqns-1. This unit is about the solution of quadratic equations. These take the form ax2 +bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs.
A quadratic function has the general form ya= axbxxc+ (where a ≠ 0 ). In this chapter we will investigate graphs of quadratic functions and, in particular, how features of the graphs relate to the coeffi cients a, b and c. A function is a rule that tells you what to do with any value you put in. We will study functions in general in chapter
Quadratic Function (Explanation & Examples) . where a, b, and c are real numbers with. , the function of the form: ff ( xx) = ꖬxx + ߾ꦐxx +cc 2. Standard Form of a Quadratic Function. The graph of is. 0 , the parabola opens up, is the minimum value of ; , the parabola opens down, is the maximum value of . ꖬ ( xx−h)2+ kk, ꖬ≠. 0.
One can write any quadratic function (1) as. f (x) = a(x ¡ h)2 + k; (Shape-Vertex Formula) b b2. where h = ¡ and k = f (h) = c ¡ . 2a 4a. EXAMPLE 1. f (x) = 2x2 ¡ 8x + 5. To derive the Shape-Vertex Formula for f (x) we ̄rst identify the coe±-cients: = 2; b = ¡8; c = ¡1: With these identi ̄cations we have: 8. = ¡ = ¡ (¡8) = = 2; 2a 2 ¢ (2) 4.
