Solve Quadratics by Graphing

Front

What are the solutions of a quadratic equation when graphed?

Back

The solutions are the x-intercepts of the graph.

Front

How do you find the solutions of a quadratic equation using its graph?

Back

Identify the points where the graph intersects the x-axis.

Front

What is another term for the solutions of a quadratic equation?

Back

x-intercepts or roots.

Front

If a quadratic equation has solutions at x = 1 and x = 3, what does this indicate about the graph?

Back

The graph intersects the x-axis at the points (1,0) and (3,0).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function.

Front

How can you determine the vertex of a quadratic function from its standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) from the standard form y = ax^2 + bx + c.

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c indicate about the graph?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/2a.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real and distinct, one real and repeated, or no real roots.

Front

How can you verify the solutions of a quadratic equation graphically?

Back

By checking if the x-values of the solutions correspond to the x-intercepts on the graph.