given the folowing quadratic equations find

the vertex
the axis of symmetry
the intercept
the domain
the range
the interval where the function is increasing andthe interval where the function is decreasing graph the function y=X^2+4x

y = (x+2)^2 - 4

you should be able to read off all the desired information from that. If you still have trouble, come on back and show where you got stuck.

To find the vertex, axis of symmetry, x-intercept, and y-intercept of a given quadratic equation, we need to use the standard form of a quadratic equation: y = ax^2 + bx + c. In this case, the given equation is y = x^2 + 4x.

1. Vertex: The vertex of a quadratic equation can be found using the formula: x = -b/2a. In our equation, a = 1 and b = 4. Plugging these values into the formula, x = -4/(2*1) = -4/2 = -2. To find the y-coordinate of the vertex, substitute the value of x back into the equation: y = (-2)^2 + 4(-2) = 4 - 8 = -4. So, the vertex is (-2, -4).

2. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex. In our case, the axis of symmetry is the line x = -2.

3. x-intercept: To find the x-intercepts, set y = 0 and solve for x. In our equation, set x^2 + 4x = 0. Factor out x to get x(x + 4) = 0. This equation is satisfied when x = 0 or x = -4. So, the x-intercepts are (0, 0) and (-4, 0).

4. y-intercept: To find the y-intercept, set x = 0 in the equation. In our equation, y = (0)^2 + 4(0) = 0. So, the y-intercept is (0, 0).

5. Domain: The domain of a quadratic function is the set of all real numbers (-∞, ∞) since there are no restrictions on the values x can take.

6. Range: The range of a quadratic function can be found by analyzing the shape of the graph. In our case, since the coefficient of x^2 (a) is positive, the parabola opens upwards, which means the range is [y-coordinate of the vertex, ∞). So, the range is [-4, ∞).

7. Intervals of Increase and Decrease: The graph of the given quadratic equation is a U-shaped parabola that opens upwards. This means the function is increasing to the left and right of the vertex, and decreasing around the vertex. So, the interval where the function is increasing is (-∞, -2) ∪ (-2, ∞), and the interval where the function is decreasing is (-2, ∞).

To graph the function y = x^2 + 4x, we can plot the vertex, x-intercepts, and y-intercept, and then draw a smooth U-shaped curve passing through these points.