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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.
An algebraic expression can change signs only at the x-values that make the expression zero or undefined. The zeros and undefined values make up the critical numbers of the expression, and they are used to determine the test intervals in solving quadratic and rational inequalities.
Quadratic Equations. 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.
Quadratic Functions. . Definition: If a, b, c, h, and k are real numbers with a 6= 0, then the functions. y = ax2 + bx + c. standard form. y = a(x − h)2 + k. vertex form. both represent a quadratic function. The graph of a quadratic function is called a parabola.
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 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.
5 Quadratic Functions. 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.
