Investigating Quadratic Functions in Vertex Form
Is y=2(x+1)2-7 a quadratic function?
yes
what is the standard form?
f(x)=ax2+bx+c
complete the square
y=x2-8x+5
y=(x-4)2-11
determine a quadratic function with each set of characteristics
vertex at (0,0), passing through the point (20, -150)
y=-0.375x2
y=2(x-1)2-2
What are a,p,q?
a=2
p=1
q=-2
what is the x-coordinate of the vertex ?
x=b/-2a
complete the square, use your answer to identity the vertex of the function
y=x2-18x-59
y=(x-9)2-140
(9,-140)
f(x)=-2x2+3x+5
identify the vertex, the axis of symmetry, the direction of opening, the maximum or minimun value
vertex (0.75, 6.125)
axis of symmetry x=0.75 open downward
maximum value of 6.125
y=2(x+1)2-3
What are the domain and range
domain:x<E
range:y>=3
f(x)=a(x-p)2+q
f(x)=ax2+bx+c
by compareing the two forms,you can see that:
b=() p=() c=() q=()
b=-2ap
p=-b/2a
c=ap2+q
q=c-ap2
determine the maximum or minimum value of the function and the value of x at which it occurs
y=3x2-12x+1
minimum value of -11 when x=2
write in vertex form
y=x2-24x+10
y=(x-12)2-134
What is quadratic function?
a function f whose value f(x) at x is given by a polynomial of degree two
f(x)=(10-3X)(4-5X)
Change it to standerd form
15X2-62X+40
correct the error（s） in the following example of completing the square
y=x2+8x+30
y=(x2+4x+4)+30
y=(x+2)2+30
y=（x2+8x+16-16）+30
y=（x+4）2+14
write quadratic function in vertex form by completing the square
y=-10x2-40x
y=-10(x+2)2+40
y=-(x-3)2+9
identify the vertex, the axis of symmetry, the direction of opening, the maximum or minimum value, and any intercepts.
vertex:3,9
axis of symmetry:x=3
opens:down
the maximum value:9
x-intercept: 0,0 6,0
y-intercept:0,0
What is the axis of symmtry?
a line through the vertex that divides the graph of a quadratic function into two congruent halves.
complete the square for the function y=ax2+bx+c
y=a(x+b/2a)2+4ac-b2/4a
what's the quadratic function in vertex form is equivalent to y=x2-2x-5
y=(x-1)2-6