Name: _________________________________________________________ Unit 3 Review

IB SL YR 1 Pd. ______ Date: __________

Unit 3 : Quadratic Functions

3-1 Factoring and solving Factoring methods( GCF, Sum/Product, DOTS, AC method) Solving Methods (Set equal to zero and Factor OR use Quad Formula OR Complete the

square.)

3-2 Discriminant b2−4 ac If ∆=0- roots are real, rational, equal If ∆>0 AND a perfect square- roots are real, rational, unequal. If ∆>0 AND not a perfect square- roots are real, irrational, unequal. If ∆<0 roots are imaginary.

3-3 Solving Quadratic Inequalities with the discriminant.1. Replace the inequality symbol with an equal sign and solve the resulting equation. The

solutions to the equation will allow you to establish intervals that will let you solve the inequality.

2. Plot the solutions on a number line creating the intervals for investigation. Pick a number from each interval and test it in the original inequality. If the result is true, that interval is a solution to the inequality.

DO THIS ONLY WHEN YOU END UP WITH AN INEQUALITY THAT HAS TWO SOLUTIONS (∆<0,∆>0)

3-4 Applications of quadraticsUse algebraic expressions to set up problems.

-Solve quadratics and ANSWER MUST MAKE SENSE.

3-5 Mixed Review- Make sure you look at answer key!

3-6 Vertex and factorized form. vertex form: y=a ( x−h )2+k vertex(h,k)

a. Don’t forget to change sign of only h coordinate when you put into equation.b. Complete the square when switching from standard form to Vertex form.

Factorized form: y=a(x−p)(x−q ). p and q are the roots.a.Don’t forget to change sign of BOTH roots when they go into equation

3-7 Equation from a graph. See what is given, choose the appropriate form, solve for a. turn back to standard form if asked to do so. to find X intercepts set y=0 and solve for x to find y intercepts set x=0 and solve for y

Equations to memorize/Know how to use!

Vertex form: y=a ( x−h )2+k vertex(h,k)

Factorized form: y=a(x−p)(x−q ). p and q are the roots.

Axis of Symmetry: x=−b2a .

Name: _________________________________ IB SL YR1 ______

Station 1: The Basics/Applications

1. Solve each equation.

a) ( x+2 )2=16

b) 3 x2+2 x−5=0

c) x2−7 x+12=0

d) x2+2x−12=0

2. Two numbers have a sum of 50 and a product of 576. Find the numbers.

Station 2: The discriminant and Quad Inequalities

1. Use the discriminant to determine the nature of the roots of:a. 2 x2−2x+3=0

2. The equation x2+2kx+3=0 has two unequal real roots. Find the possible values of k .

3. Find the values of p such that the equation has two different real roots.

x2+4 x+ p=0

4. Find the values of m such that the equation has no real roots.

x2+5mx+25=0

Station 3: The Forms of the quadratic (vertex, factorized, standard)

1. Let f ( x )=a ( x−p ) (x−q ). Part of the graph of f is shown below. The graph passes through the points (−5 ,0 ) , (1,0 ) and (0 ,10 ).

a. Write down the value of p and q.

b. Find the value of a.

2. Let f ( x )=a ( x+3 )2−6.

a. Write down the coordinates of the vertex of the graph of f .

b. Given that f (1 )=2, find the value of a.

c. Hence find the value of f (3).

3. Let f ( x )=2x2+12x+5.

a. Write the function f , giving your answer in the form f ( x )=e ( x−n )2+ p.

b. The graph of g is formed by translating the graph of f by 4 units in the positive x-direction and 8 units in the positive y-direction. Find the coordinates of the vertex of the graph of g.

4. The function f (x) is defined as f (x) = –(x – h)2 + k. The diagram below shows part of the graph of f (x). The maximum point on the curve is P (3, 2).

a. Write down the value of

(i) h;

(ii) k;

b. Show that f (x) can be written as f (x) = –x2 + 6x – 7.

4

2

– 2

– 4

– 6

– 8

– 1 0

– 1 2

– 1 1 2 3 4 5 6x

y

P (3 , 2 )

5. Let f ( x )=2x2−12 x+5

a) Express f (x) in the form f ( x )=2(x−h)2+k

b) Write down the equation of the axis of symmetry of the graph of f .

c) Write down the vertex of graph f.

d) Find the y- intercept of th graph of f.

Station 4: Graphs of Quadratics1. Use the vertex, axis of symmetry and y-intercept to sketch:a) y=(x−2)2−4

b) y=−12

(x+4)2

+6

2. Solve for the x intercepts of the quadratic y=3 x2+4 x−7.

3. Considerf ( x )=(x+1)2−4. Find:

a) The x intercepts

b) The y-intercepts

c) What are the coordinates of the minimum of the function?

4. Let f ( x )=x2+3 x−4 . Part of the graph of f is shown below.

a. Write down the y-intercept of the graph of f .

b. Find the x-intercepts of the graph.

c. Write down the equation of the axis of symmetry.

d. Write down coordinates of the vertex of the graph of f .

4

2

– 2

– 4

– 6

– 4 – 2 0 2 4 6 x

y

A B

Station 5: Equations from Graphs

1. Write the equation of the quadratic function shown in the graph. Give your answer in the form y=a x2+bx+c.

2. The equation of a curve may be written in the form y = a(x – p)(x – q). The curve intersects the x-axis at A(–2, 0) and B(4, 0). The curve of y = f (x) is shown in the diagram below.

a. Write down the value of p and of q.

b. Given that the point (6, 8) is on the curve, find the value of a.

c. Write the equation of the curve in the form y = ax2 + bx + c.

3. Write the equations of the graphs shown. Express your answers in the form y=a x2+bx+c .

4. A quadratic function has a vertex (−1 ,−5), and one of its zeros is 4. Find the equation of the function in the form y=a x2+bx+c .