Question

y=4x^2-3 compare to the graph of y=4x^2?

The graph of y=4x^2=-3 is....
a graph with 2 slopes going downward one is longer then the other the red one is smaller the blue one is longer with an equation of y=4x^2-3 and the red one y=4x^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

- The graph of y=4x^2-3 is shifted downwards by 3 units compared to the graph of y=4x^2.

- Both graphs are parabolas that open upwards.
- The graph of y=4x^2-3 intersects the y-axis at y=-3, while the graph of y=4x^2 intersects the y-axis at the origin (0,0).
- The vertex of the graph of y=4x^2-3 is at (0,-3), while the vertex of the graph of y=4x^2 is at the origin (0,0).

Answer 2

the answers are

shifted up
shifted down
the same height

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in my previous response. The correct comparison is as follows:

- The graph of y=4x^2-3 is shifted down by 3 units compared to the graph of y=4x^2.
- Both graphs are parabolas that open upwards.
- The vertex of the graph of y=4x^2-3 is at (0,-3), while the vertex of the graph of y=4x^2 is at the origin (0,0).

Answer 4

How long will it take the ball to reach its maximum height?

AND

What is the ball's maximum height?

it will take 2 seconds to reach a max height of 20 ft
it will take 1 seconds to reach a max height of 20 ft
it will take 20 seconds to reach a max height of 1 ft
it will take 20 seconds to reach a max height of 2 ft

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct answer is: It will take 1 second to reach a maximum height of 20 ft.

Explanation:
When an object is thrown upwards, it reaches its maximum height at the midpoint of its journey, before it starts descending. The time taken to reach maximum height for a projectile thrown vertically upward can be calculated by the formula t = V0/g, where V0 is the initial vertical velocity and g is the acceleration due to gravity.

In this case, the time taken to reach maximum height is:
t = (0 m/s)/(-9.81 m/s^2) = 1 second

Therefore, it will take 1 second for the ball to reach a maximum height of 20 ft.

Answer 6

what is the correct answer

Answer 7

[AI-generated answer — Bot GPT 3.5]

The correct answer is: It will take 1 second to reach a maximum height of 20 ft.

Explanation:
The time taken to reach the maximum height of a projectile launched vertically upward can be determined by the formula t = V0/g, where V0 is the initial velocity and g is the acceleration due to gravity (-9.81 m/s^2).

Given that the object reaches a maximum height of 20 ft, we need to convert this to meters for consistency with the acceleration due to gravity. 20 ft is approximately 6.1 meters.

Thus, the time taken to reach the maximum height is:
t = (0 m/s)/(-9.81 m/s^2) = approximately 1 second

Therefore, it will take 1 second for the ball to reach a maximum height of 20 ft (approximately 6.1 meters).

Answer 8

The graph of a quadratic function is shown. What is the axis of symmetry?

(Be sure to move the line on the graph AND type in the equation below to get full credit on this question).

Drag the dot on the vertical line to the location that represents the axis of symmetry.

Answer 9

[AI-generated answer — Bot GPT 3.5]

I'm unable to view or interact with images or graphs. However, to determine the axis of symmetry for a quadratic function represented by the graph, you should look for the vertical line that passes through the vertex of the parabola.

The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It is equidistant from the two arms of the parabola and passes through the vertex.

To find the equation of the axis of symmetry, you need to identify the x-coordinate of the vertex (h) from the graph, and the axis of symmetry will be the vertical line x = h.

Once the vertex is located and the axis of symmetry is identified, the equation of the axis of symmetry can be written as x = h, where h is the x-coordinate of the vertex.

Answer 10

0=-5x^2+3x+2

Answer 11

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation 0 = -5x^2 + 3x + 2, you can use the quadratic formula or factorization method.

1. Using the quadratic formula:
The quadratic formula states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a

In your case, the quadratic equation is -5x^2 + 3x + 2 = 0, so a = -5, b = 3, and c = 2. Plugging these values into the quadratic formula, we get:
x = (-3 ± √(3^2 - 4*(-5)*2)) / (2*(-5))
x = (-3 ± √(9 + 40)) / -10
x = (-3 ± √49) / -10
x = (-3 ± 7) / -10

This results in two solutions:
x = (-3 + 7) / -10 = 4 / -10 = -0.4
x = (-3 - 7) / -10 = -10 / -10 = 1

Therefore, the solutions to the quadratic equation -5x^2 + 3x + 2 = 0 are x = -0.4 and x = 1.

2. Using factoring:
Another method to solve the quadratic equation is by factoring. You would factor the quadratic equation and set each factor equal to zero:
-5x^2 + 3x + 2 = 0
(-5x + 2)(x + 1) = 0

From this factored form, you get:
-5x + 2 = 0 -> -5x = -2 -> x = -2/5
x + 1 = 0 -> x = -1

Therefore, the solutions using factoring are x = -2/5 and x = -1.