Answer:
Solving Quadratic Equations by Graphing:
The graph of a quadratic equation is a parabola.
The solutions (or roots) of the equation correspond to the x-intercepts of the parabola. These are the points where the parabola intersects the x-axis (y = 0).
Steps to solve a quadratic equation by graphing:
Rewrite the equation in vertex form (y = a(x - h)^2 + k) if not already given in that form. This vertex form reveals the vertex's location (h, k) of the parabola.
Plot the vertex point (h, k).
The parabola is symmetrical around the vertical line passing through the vertex. So, if you plot one point to the left of the vertex, its mirror image on the right side must also be on the parabola.
Continue plotting additional points to the left and right of the vertex to form the shape of the parabola.
The x-intercepts (where the parabola intersects the x-axis) are the solutions of the quadratic equation.
Key takeaway:
By graphing the quadratic equation, the solutions can be visualized as the x-intercepts of the parabola. These points correspond to the values of x that make the function zero (y = 0).
Step-by-step explanation:
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