Find the quadratic function for the parabola given in the graph. Write an inequality that describes the shaded region.

A standard form of quadratic function is f ( x ) = a ( x - h ) 2 + k , where h , k is called the vertex of the parabola From the given graph, we can observe h , k = 1 , 3 Therefore, quadratic function is f ( x ) = a ( x - 1 ) 2 + 3 Now, we need to find the value of a , by substituting any point from the graph From the graph we can observe, a graph is passing through the point - 2 , 0 ⇒ 0 = a ( - 2 - 1 ) 2 + 3 ⇒ a = - 1 3 Therefore, the required quadratic function that models the parabolic arch of the dam is f ( x ) = - 1 3 ( x - 1 ) 2 + 3 In the given graph a parabola is a dotted line, So we need to use strict inequalities Therefore, y < - 1 3 x - 1 2 + 3 or y > - 1 3 x - 1 2 + 3 Test a point chosen from the shaded region to above inequalities Substitute a point 5 , 0 in y < - 1 3 x - 1 2 + 3 , we get 0 < - 1 3 5 - 1 2 + 3 0 < - 16 3 + 3 0 < - 7 3 is not true Therefore, y > - 1 3 x - 1 2 + 3 represents the shaded region

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>Go Ahead and Log In>Chapter 17 - Non-Linear Inequalities>Practice 3

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 8: Practice 3

Author:Rose Harrison, Clara Huizink, Aidan Sproat Clements & Marlene Torres Skoumal

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 8: Practice 3

Attempt the practice questions from Exercise 8: Practice 3 with hints and solutions to strengthen your understanding. Extended MYP Mathematics A Concept based approach Years 4 & 5 solutions are prepared by Experienced Embibe Experts.