Review for EOC Algebra

1) In the quadratic equation x² – x + c = 0, c represents an unknown constant. If x = -4 is one of the solutions to this equation, what is the value of c? (-4)² - (-4) + c = c = 0 c = -20 What is the other solution to the equation? 0 = x² - x = (x - 5)(x + 4) x = 5 and -4

2) What is the vertex and the roots of y = x² – 9? “roots” of the equation are the x-intercepts …when y = 0 0 = x² - 9 can factor 0 = (x + 3)(x – 3) Check the graph or the table : Vertex (0, -9) Roots are at 3 and -3 on x-axis

3) Given the function f(x) = -4x² - 6, what is the value of f(-3)? What is the value of the function when x is -3? f(-3) = -4(-3)² - 6 f(-3) = -42 f(-3) = f(-3) = input output Or … put equation in Y = -4x ² - 6 And check the table

7(x – 1) – 4(x – 3) = 17 7x – 7 – 4x + 12 = 17 distribute subtract 5 from both sides 3x + 5 = 17 combine like terms 3x = 12 3x = 12 divide both sides by 3 3 x = 4 4)

x + 6 x 5) The area of a rectangle is 16 square centimeters. The length is 6 more than the width. Set up and solve an equation to find the length of the rectangle Area = length width 16 = (x + 6)x Or … x² + 6x = 16 Quadratic Equation

1) FACTORING METHOD 2) Quadratic Formula 3) Graphing x 2 + 6x = 16 need to set the equation = 0, by moving 16 to other side Gives you the: x-intercepts the roots of the equation the zeroes of the function -16 x 2 + 6x – 16 = 0 (x - 2)(x + 8) = 0 factor the trinomial x - 2 = 0? x + 8 = 0? ask yourself what makes each factor = 0 x = 2 and x = -8 but for width, can not use the negative answer

The area of a rectangle is 16 square centimeters. The length is 6 more than the width. Set up and solve an equation to find the length of the rectangle x + 6 x Substitute x = 2 in for the length The length is 8 cm

6) Solve the Equations: 1) 4x + 16 = 20 Linear – subtract a 16 from both sides, then divide by 4 on both sides x = 1 Quadratic – already factored, ready to solve, what makes each factor = 0? x = -½, and 5 Quadratic – needs to be factored Pull out GCF 3x(x + 2) = 0 Now figure what makes each factor = 0, x = 0 and -2 2) (2x + 1)(x - 5) = 0 3) 3x 2 + 6x = 0

7) What is the range of the function? Smallest ………………….Largest Is ‘range’ the x-values or the y-values? y Does the graph include -3 ? Yes ≤, No < ≤ Does the graph include 4 ? Yes ≤, No < ≤ -34

8) What is the domain of the function? Smallest ………………….Largest Is ‘domain’ the x-values or the y-values? x Does the graph include 0 ? Yes ≤, No < < Does the graph include 6 ? Yes ≤, No < ≤ 60

9)Use the quadratic formula to solve for the zeroes of the function: Y = 2x ² – 4x – 10 Identify : a= ____ b = _____ c = ______ Fill in the formula :

Y = 2x ² – 4x – 10 Simplify : Put in calculator to get both answers : __________ and __________ Find the vertex of this parabola: (, ) 1 -12

10) Identify each of the following from the graph: a)The line of symmetry ___________ b) The zeroes of the function ___________ c) The vertex ___________ d) The number of real roots _______ e) The parent function: ___________ x = 2 -1 and 5 y = x ² 2 (2, -9)

11)Which parent function to the following set of points belong? {(-4, 5) (-2, 3) (0, 1) (2, -1) (4, -3) } Plot the points !!! What is the equation of the line through the points? y = -x + 1

12) Name the type of graph for each CHOICES: Linear Quadratic Exponential Inverse Variation Direct Variat ion AB C D E Exponential Quadratic Linear & Direct Variation Inverse Variation Linear