Quadratic function

QUADRATIC FUNCTION

QUADRATIC FUNCTION

It´s a polynomial function of second degree, whose graph is a curve called parabola.

Where a,b and c are constan, c is the interts, a≠0 , c is the y-intercept.

cbxxaxf 2)(

VERTEX FORM OF THE QUADRATIC FUNCTION

(y-k)=(x-h)2

Where (h,k) are the coordinates of the vertexSimmetry axis

Vertex (h,k)

The coordinate x of the vertex (the h value) is

a

bx

2

The coordinate y of the vertex (the k value) is f(h)

The vertex can be a maximum value or a minimum value.

The vertex is maximum if the parabola opens downwards a<0

The vertex is minimum if the parabola opens upwards a>0

Solve: f(x)= -x2+2x+8 a=-1 b=2 c=8

A) Find the roots(x intercepts)B) Find the vertexC) Find the y-interceptD) Write the equation of the symmetry axisE) Sketch the graph

A)0=-x2+2x+8 0=-(x2-2x-8) 0=(x2-2x-8)0=(x-4)(x+2) Roots are x=4, x=-2

B) Find the vertex(h,k)h= -b/2 a = -(2)/2(-1) = 1k= f(h)= -(1)2+2(1)+8 = 9

C) Find the y-intercept c=8

D) Write the equation of the symmetry axis x=1

E) Sketch the graph

SOLVE F(X)= 3X2-9X-12

A) Find the roots(x intercepts) B) Find the vertex C) Find the y-intercept D) Write the equation of the symmetry

axis E) Sketch the graph f(x)= 3x2-9x-12 f(x)= x2-4x+4 f(x)= -16x2+256x

f(x)= 3x2-9x-12

f(x)= x2-4x+4

f(x)= -16x2+256x

Which of the following equations corresponds to the next graph?

)4)(6(1.0)

)2)(6(5.0)

)4)(6(1.0)

)4)(2(5.0)

xxyd

xxyc

xxyb

xxya

Match each equation with the corresponding graph

x

x

x

x

yd

yc

yb

ya

2

2

2

2

5.2)

2.0)

5.0)

5.0)

FIND ELEMENTS OF THE PARABOLA

4)2(5.0)

4)2(5.0)

4)2(5.0)

4)2(5.0)

2

2

2

2

xyd

xyc

xyb

xya