Precalculus

What is the vertex of f(x) = 2(x+5)^2 - 3?

(-5, -3)

What is the axis of symmetry for f(x) = 2(x+5)^2 - 3?

x = -5

For f(x) = 2(x+5)^2 - 3, does it open up or down, and is it wider or narrower than the parent parabola?

Opens up; narrower than the parent (a = 2 > 1)

For f(x) = -0.8(x-1)^2 + 7, what is the vertex, axis of symmetry, opening, and width?

Vertex (1, 7); axis x = 1; opens downward; width wider than the parent (|a| = 0.8 < 1)

In f(x) = 2x^2 + 12x + 10, what is the y-intercept?

10

In f(x) = 2x^2 + 12x + 10, what is the axis of symmetry?

x = -3

In f(x) = 2x^2 + 12x + 10, what is the vertex?

(-3, -8)

For f(x) = -x^2 - 4x + 5, what is the vertex, axis of symmetry, opening, and width?

Vertex (-2, 9); axis x = -2; opens downward; width standard (|a| = 1)

Write f(x) = x^2 + 8x + 10 in vertex form.

f(x) = (x+4)^2 - 6

For f(x) = -3x^2 + 18x - 20, what is its maximum value and at what x?

Maximum value 7 at x = 3

Which function has a greater maximum value if you compare f(x) = -2x^2 + 12x - 10 with another function g(x) whose maximum is 10?

Compare their vertex y-values. For f(x), the vertex is (3, 8), so its maximum is 8. If g(x) has a maximum of 10, then g(x) has a greater maximum value.

For h(t) = -16(t-2)^2 + 80, what are the object's initial and maximum heights?

Maximum height: 80; initial height (at t = 0): 16

What is the vertex of f(x) = 2(x+5)^2 - 3?

(-5, -3)

What is the axis of symmetry for f(x) = 2(x+5)^2 - 3?

x = -5

For f(x) = 2(x+5)^2 - 3, does it open up or down, and is it wider or narrower than the parent parabola?

Opens up; narrower than the parent (a = 2 > 1)

For f(x) = -0.8(x-1)^2 + 7, what is the vertex, axis of symmetry, opening, and width?

Vertex (1, 7); axis x = 1; opens downward; width wider than the parent (|a| = 0.8 < 1)

In f(x) = 2x^2 + 12x + 10, what is the y-intercept?

10

In f(x) = 2x^2 + 12x + 10, what is the axis of symmetry?

x = -3

In f(x) = 2x^2 + 12x + 10, what is the vertex?

(-3, -8)

For f(x) = -x^2 - 4x + 5, what is the vertex, axis of symmetry, opening, and width?

Vertex (-2, 9); axis x = -2; opens downward; width standard (|a| = 1)

Write f(x) = x^2 + 8x + 10 in vertex form.

f(x) = (x+4)^2 - 6

For f(x) = -3x^2 + 18x - 20, what is its maximum value and at what x?

Maximum value 7 at x = 3

Which function has a greater maximum value if you compare f(x) = -2x^2 + 12x - 10 with another function g(x) whose maximum is 10?

Compare their vertex y-values. For f(x), the vertex is (3, 8), so its maximum is 8. If g(x) has a maximum of 10, then g(x) has a greater maximum value.

For h(t) = -16(t-2)^2 + 80, what are the object's initial and maximum heights?

Maximum height: 80; initial height (at t = 0): 16

What is the vertex, axis of symmetry, opening, and width for f(x) = -3(x-4)^2 + 1?

Vertex (4, 1); axis x = 4; opens downward; narrower than the parent (|a| = 3 > 1)

For f(x) = -x^2 + 6x - 2, what is the y-intercept, axis of symmetry, and vertex?

y-intercept -2; axis x = 3; vertex (3, 7)

Write f(x) = -2(x+1)^2 + 5 in standard form.

f(x) = -2x^2 - 4x + 3

What is the minimum value for f(x) = 3x^2 - 6x + 2 and at what x?

Minimum value -1 at x = 1

A ball is thrown upward with a velocity of 24 ft/s from a 6-foot platform. The function describing its height is h(t) = -16t^2 + 24t + 6. What is the maximum height the ball reaches and when does it occur?

Maximum height 15 feet at t = 0.75 seconds

A rectangular garden is to be fenced on three sides with 40 feet of fencing, with a house forming the fourth side. What dimensions will maximize the area of the garden?

Length parallel to the house is 20 feet, and the other two sides are 10 feet each. Maximum area is 200 sq ft.

The profit (in hundreds of dollars) for selling x units of a product is given by P(x) = -0.05x^2 + 10x - 300. How many units should be sold to maximize profit, and what is the maximum profit?

100 units should be sold for a maximum profit of 200 (which means $20,000).

axis of symmetry for (x - h)² = 4p(y - k)

x = h

focus for (x - h)² = 4p(y - k)

(h, k + p)

directrix for (x - h)² = 4p(y - k)

y = k - p

axis of symmetry for (y - k)² = 4p(x - h)

y = k

focus for (y - k)² = 4p(x - h)

(h + p, k)

directrix for (y - k)² = 4p(x - h)

x = h - p