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A quadratic equation is a second-degree polynomial equation in a single variable, usually written as a x^2 + bx + c = 0 where a ≠ 0.Key characteristics:• The graph of a quadratic equation is a parabola.• The coefficient 'a' determines the direction (upward if a > 0, downward if a < 0).• It can have zero, one, or two real solutions.In the exercise, the quadratic equation given is already in the vertex form, y = -(x + 3)^2, an example of a quadratic equation.

The vertex form of a quadratic equation is y = a(x - h)^2 + k,where (h, k) is the vertex of the parabola.Important elements:

• The vertex is the highest or lowest point on the graph, depending on the parabola's direction.
• The coefficient 'a' determines the width and direction of the parabola. The parabola gets narrower as |a| increases.
• If 'a' is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

For the given exercise:

• The equation y = -(x + 3)^2 shows the vertex form with h = -3 and k = 0.
• Therefore, the vertex is at (-3, 0).

Understanding the vertex form helps in easily graphing the quadratic equation and identifying the vertex.

Intercepts are points where the graph crosses the axes.

• Y-Intercept is where the graph crosses the y-axis (x = 0).
• X-Intercepts are where the graph crosses the x-axis (y = 0).

In the exercise, y = -(x + 3)^2, we find the intercepts as follows:**Y-Intercept**: Set x = 0 and solve for y:y = -(0 + 3)^2 = -9, so the y-intercept is (0, -9).**X-Intercepts**: Set y = 0 and solve for x:0 = -(x + 3)^2gives us x = -3, so the x-intercept is (-3, 0).We use these intercepts to sketch the graph, along with the vertex and direction.