Function Features
What is the vertex of
f(x) = -2(x+2)2
Vertex: (-2, 0)
Write the equation of a parabola (x2) that is shifted to the right 3 and up 2
y = (x-3)2+2
(x + 7) (x - 6)
x2 + x - 42
2-12x
2(1-6x)
Just factor.
x2 + 5x + 4
(x + 4)(x + 1)
What is the vertex and axis of symmetry for the function:
f(x) = 2(x-1)2 - 3
Vertex: (1, -3)
AoS: x = 1
Write the equation of a parabola (x2) that is vertically stretched by 2 and shifted one down
y = 2x2 - 1
Solve for a
4 = a(-3 + 7)2 - 28
a = 2
8x2-x
x(8x-1)
Factor and solve.
x2 + 2x - 80
(x - 8)(x + 10)
x = 8, -10
What is the vertex, axis of symmetry, and min/max of the function
f(x) = 3(x - 1)2 + 2
Vertex: (1, 2)
AoS: x=1
Min: y=1
Write the equation of a parabola (x2) that is reflected over the x-axis, shifted to the left 3, and down 4
y= - (x2 + 3) - 4
A parabola has a vertex of (1, 20) and passes through (0, 4). Solve for a
a = -16
27x5-24x4
3x4(9x-8)
Just factor.
3x2 + 4x + 1
(3x + 1)(x + 1)
What is the vertex, axis of symmetry, min/max, and y-intercept of the function
f(x) = — (x+4)2 - 5
Vertex: (-4, -5)
AoS: x = -4
Max: y = -5
Y-Intercept: (0, -21)
Write the equation of a parabola (x2) that is vertically shrunk by 1/2, shifted 5 units to the right, and 2 units up
y = 1/2(x - 5)2 + 2
A parabola with a vertex of (2, 10) passes through the point (0, 4). Write the vertex form equation 😟
y = -3/2 (x - 2)2 + 10
-3x3-x
-x(3x2+1)
Factor and solve.
2x2 - 11x + 5 = 0
(2x - 1)(x - 5)
x = 1/2, 5
What is the vertex, axis of symmetry, min/max, y-intercept, domain, and range of the function
f(x) = — (x+1)2 + 7
Vertex: (-1, 7)
AoS: x = -1
Y-Intercept: (0, 6)
Domain: (-inf, inf)
Range: (-inf, 7)
Write the equation of a parabola (x2) that is reflected over the x-axis, vertically stretched by 8, shifted 3 units to the left, and shifted 5 down
y = -8(x + 3)2 - 5
A parabola with the vertex (1, 2) passes through the point (0, 4). Write the equation in standard form 😨
y = 2x2 - 4x + 4
25x2-100
25(x+2)(x-2)
Factor and solve.
4x2 - 8x - 140 = 0
4(x - 7)(x + 5)
x = -7, 5