Answer :

to find the x intercept, you have to find the part that will be crossing the x axis if you put it on a graph. to find the y intercept you have to find the part of the equation that will be crossing the y axis if you put it on a graph. The axis of symmetry is the line that divides a parabola into two parts that are mirror images. If the parabola opens up or down, the axis of symmetry is vertical. If the parabola opens right or left, the axis of symmetry is horizontal. The vertex is the point where the axis of symmetry intersects the parabola.

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Rewritten by : Barada

Final answer:

The x-intercept(s) is/are found by setting y to zero and solving for x in the equation. The y-intercept is found by setting x to zero and solving for y. The axis of symmetry can be computed using the equation x = -b / 2a, while the vertex is found by substituting x = -b / 2a back into the equation to find the corresponding y-value.

Explanation:

Let's discuss the mathematical entity called a 'quadratic function', often represented by y = ax^2 + bx + c. Certain elements from this model can reveal a great deal about the function's graph.

  1. X-Intercept: The x-intercepts are the points at which the graph touches or crosses the x-axis. To find these points, you set y to zero and solve for x.
  2. Y-Intercept: The y-intercept is the point where the graph crosses the y-axis. To find this point, you simply need to substitute x with zero in your equation and solve for y, yielding 'b' in your equation.
  3. Axis of Symmetry: The axis of symmetry is the vertical line that divides the parabola into two equal halves. The formula is x = -b / 2a.
  4. Vertex: The vertex of a parabola is the point at which the graph reaches its maximum or minimum value. If the parabola opens upwards, the vertex is the minimum point. If the parabola opens downwards, the vertex is the maximum point. The vertex is found on the axis of symmetry at point ( -b / 2a , f(-b / 2a) ).

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