Quadratic Functions

JJ

100

The standard form of a quadratic equation is ax²+bx+c=0.

Identify the values of a, b and c in the quadratic equation −8x²+3x=0.

a = -8

b = 3

c = 0

200

Express 9−√−64 in terms of i

9-8i

300

Consider the equation y=2x². (5)

Is every value of y positive?

State the axis of symmetry of the parabola.

What is the minimum value of y?

Yes

x = 0

(0,0)

400

Identify the graph of the quadratic f(x)=ax²+bx+c, where a>0 and b2−4ac=0

(13)

C

500

Solve the equation 4x²+6x+2=0 using the quadratic formula.

-1/2

-1

Yoyo

100

The standard form of a quadratic equation is ax²+bx+c=0.

Identify the values of a, b and c in the quadratic equation 3x²−8x+2=9x−7.

a = 3

b = -17

c = 9

200

Express −√−100 in terms of i.

-10i

300

A quadratic function includes the points shown in the table. (4)

Does the function have a maximum or minimum point?

What is the minimum value of the function?

What is the range of the function?

Minimum

(7,-3)

y ≥ -3

400

Below your discriminant from the quadratic formula.

d = 9-4x56

How many solutions will there be?

2 imaginary or no real solutions

500

Solve x²+2x+5=0, stating your solutions in the form a±bi

-1±2i

TomTom

100

By definition, what is the number i equal to?

Therefore, what does i² equal?

√−1

-1

200

Consider a quadratic function that passes through the points shown in the table. (3)

Does this quadratic function have a maximum or minimum point?

What is the minimum value of the function?

What is the range of the quadratic function?

Minimum

(4,-1)

y ≥ -1

300

Consider the graph of the function y=f(x) and answer the following questions. (2)

What is the absolute minimum of the graph?

Hence determine the range of the function.

Over what interval of the domain is the function decreasing?

(-4,0)

y≥0

x<-4

400

For a particular quadratic equation, ax²+bx+c=0, b2−4ac=0, how many solutions are there?

No real solutions

(or 2 imaginary ones)

500

Use the quadratic formula to find the solutions of x²+7x−3=0.

-0.46

-6.54

Cody

100

To solve x²−x=2, Emma substitutes a=1 into the quadratic formula. What value of c should she substitute into the quadratic formula?

-2

200

Consider the curve y=x²+2x−2.

Determine the equation of the axis of symmetry.

Now determine the minimum value of y.

x = -2/2 = -1

(-1,-3)

300

After using your quadratic formula, your discriminant is -1, how many solutions will there be?

No real solutions or 2 imaginary

400

Consider the equation x²+6x+9=0

Find the discriminant and number of solutions.

0

1 solution

500

Solve the equation x²+11x+28=0 by using the quadratic formula.

-1

-10