Describe
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=(x-5)2
The function f had a horizontal translation 5 units right.
What is the formula for quadratics in vertex form?
f(x)=a(x-h)2+k
What is the equation for quadratics in standard form?
f(x)=ax2+bx+c
What is the equation for quadratics in intercept form?
f(x)=a(x-p)(x-q)
What is the formula to find the focus?
a=1/(4p)
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=(x+3)2-1
The function f had horizontal translation of 3 units left and a vertical translation of 1 unit down.
What is the vertex and axis of symmetry? Graph the function.
f(x)=(x-3)2+4
Vertex(3,4)
Axis of symmetry: x=3
What is the formula to find the axis of symmetry when in standard form?
x= (-b)/2a
Find the x-intercepts, vertex, and axis of symmetry. Graph the function.
f(x)=(x+2)(x-4)
Vertex:(1,-9)
Axis of Symmetry: x=1
X intercepts: (-2,0) & (4,0)
Find the focus and the vertex. Graph the function and the focus.
f(x)=1/8x2
Focus: (0,2)
Vertex: (0,0)
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=3(x-4)2
The function f had a horizontal translation 4 units right and a vertical stretch of 3.
What is the vertex and axis of symmetry? Graph the function.
f(x)=(x+4)2-2
Vertex: (-4,2)
Axis of symmetry: x=-4
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= x2-8x+12
vertex (4,-4)
Axis of symmetry: x=4
y-intercept:(0,12)
Find the x-intercepts, vertex, and axis of symmetry. Graph the function.
f(x)=-(x-2)(x+4)
Vertex:(-1,9)
Axis of symmetry: x=-1
X intercepts:(2,0) & (-4,0)
Find the focus and the vertex. Graph the function and the focus.
f(x)=1/24x2
Focus: (0,6)
Vertex: (0,0)
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=1/2x2+7
The function f had vertical shrink of 1/2 and a vertical translation of 7 units down.
What is the vertex and axis of symmetry? Graph the function.
f(x)= -2(x+1)2
Vertex: (-1,0)
Axis of Symmetry: x=-1
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= -x2-8x-15
Vertex: (-4,1)
Axis of symmetry: x=-4
y intercept: (0,-15)
Find the x-intercepts, vertex, and axis of symmetry. Graph the function.
f(x)=2(x+3)(x-1)
Vertex: (-1,-8)
Axis of symmetry: x=-1
X intercepts: (-3,0) & (1,0)
Find the focus and the vertex. Graph the function and the focus.
f(x)=1/16(x-3)2+1
Focus: (3,5)
Vertex: (3,1)
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=-4(x-6)2-2
The function f had a vertical stretch of 2 and reflected over the x-axis. The function had a vertical translation of 2 units down and a horizontal translation of 6 units right.
What is the vertex and axis of symmetry? Graph the function.
f(x)=1/3x2+2
Vertex: (0,2)
Axis of symmetry: x=0
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= 2x2+4x-6
Vertex: (-1,-8)
Axis of Symmetry: x=-1
y intercept: (0,-6)
Find the x-intercepts, vertex, and axis of symmetry. Graph the function.
f(x)=-1/2(x+2)(x-4)
Vertex: (1, 4.5)
Axis of symmetry: x=1
X intercept: (-2,0) & (4,0)
Find the focus and the vertex. Graph the function and the focus.
f(x)=16(x+2)2-5
Focus: (-2,-5 1/64)
Vertex:(-2,-5)