Quadratic Graphs definition

Question 1

What is the shape of a quadratic function

ax² + bx + c

Answer 1

It is in the shape of a parabola (U shaped curve)

It is symmetrical about a line

Question 2

When a is positive, is the graph U shaped or inverted U shape?

ax² + bx + c

Answer 2

It is a U shaped curve

for example

2x² + x + 3

x² - x - 3

Question 3

When a is negative, is the graph U shaped or inverted U shape?

ax² + bx + c

Answer 3

It is inverted U shaped curve

for example

• 2x² + x + 3
• x² - x - 3

Question 4

Where is the turning point of the quadratic graph when

a is positive

ax² + bx + c

Answer 4

It is where the curve changes its direction

When a is positive, this point is called the minimum point

The minimum point lies on the line of symmetry

Question 5

Where is the turning point of the quadratic graph whe

a is negative

ax² + bx + c

Answer 5

It is where the curve changes its direction

When a is negative, this point is called the maximum point

The maximum point lies on the line of symmetry

Question 6

Why do we say that x = -2 and x = 2 is the solution of the quadratic equation x² - 4 = 0

Answer 6

When x = -2

(-2)² - 4 = 0

When x = 2

(2)² - 4 = 0

The LHS of both equations = RHS of both equation

Question 7

From the graph. how do we observe that

x = -2 and x = 2

is the solution of the quadratic equation x² - 4 = 0

Answer 7

The graph intersects the x -axis at x = -2 and x = 2

The equation of the x-axis is y = 0