4-1
Graph f(x) = x2 - 4x + 3, labeling the y-intercept, vertex, and axis of symmetry.
y - intercept = 3
vertex = (2, -1)
axis of symmetry: x = 2
Solve by factoring: 3x2 - x = 4
{-1, 4/3}
Identify the axis of symmetry, vertex, and direction of opening for y = -(x-6)2 - 5
Axis of symmetry: x = 6
Vertex: (6, -5)
Direction: down
Name the vertex y= (x-3)^2 +4
(3,4)
Write an equation for the parabola:
Vertex = (0,0)
Focus = (0, (-1/12))
y = -3(x-0)2 + 0
Determine if f(x) = 5x2 - 20x + 3 has a maximum or minimum and find that value.
Minimum = -17
Solve by completing the square:
x2 - 8x + 14 = 0
4 plus or minus the square root of 2
Write an equation for the parabola with vertex at (-4,2) and y-intercept -2
y = (-1/4)(x+4)2 + 2
Name the vertex: y= (x+1)^2 - 8
(-1, -8)
Write an equation for the parabola:
Vertex = (5,1)
Focus = (5, (5/4))
y = (x-5)2 + 1
Solve x2 + 2x - 3 = 0 by graphing and determine the vertex.
Vertex = (-1, -4)
Solutions {1, -3}
Solve the equation by the square root property:
9x2 + 12x + 4 = 6
(-2 plus or minus the square root of six) / 3
Write y = x2 + 4x + 8 in vertex form.
y = (x+2)2 +4
Solve 2x2 - 7x - 15 < 0 algebraically
((-3/2), 5)
Write an equation for the parabola:
Vertex = (1,3)
Directrix: x = 7/8
x = 2(y-3)2 + 1
This is the number before the x2 that determines whether a parabola opens up or down.
Leading coefficient
Find the exact solutions by using the Quadratic Formula:
2x2 = 9x -5
(9 plus or minus the sq root of 41) / 4
Graph y ≥ x2 - 4x +4
See graph
Write the equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of parabola.
y = x2 + 2x + 2
y = (x+1)2 +1
Vertex: (-1,1)
Axis of symmetry: x = -1
Direction: up
Graph the equation. Must include vertex, and at least one point on each side. y=(x-4)^2 + 3
The line that runs through the vertex and divides the parabola in half.
Axis of symmetry
What form is this equation in?
y = - 1/2 (x + 7) - 4
Vertex form
The height, h (in feet), of a certain rocket t seconds after it leaves the ground is modeled by
h(t) = -16t2 + 64t + 12.
Write the function in vertex form and find the maximum height reached by the rocket.
h(t) = -16(t-2)2 +76
Max height: 76 feet
Write the equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of parabola.
y = -2x2 + 12x - 14
y = -2(x-3)2 + 4
Vertex: (3,4)
Axis of symmetry: x = 3
Direction: down
What is the equation for the axis of symmetry?
x = -b/2a