Quadratic function
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QUADRATIC FUNCTION
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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)(
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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)
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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
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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
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E) Sketch the graph
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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
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f(x)= 3x2-9x-12
f(x)= x2-4x+4
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f(x)= -16x2+256x
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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
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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)
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FIND ELEMENTS OF THE PARABOLA
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4)2(5.0)
4)2(5.0)
4)2(5.0)
4)2(5.0)
2
2
2
2
xyd
xyc
xyb
xya