Solve Quadratics by Graphing

Front

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

Back

x-intercepts

Front

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

Back

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

Front

What are the points where a quadratic graph intersects the x-axis called?

Back

x-intercepts or solutions

Front

What does it mean if a quadratic graph does not intersect the x-axis?

Back

It has no real solutions.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal to 0 by subtracting 3 from both sides.

Front

What is the standard form of a quadratic equation?

Back

ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph of the quadratic.

Front

How can you find the vertex of a quadratic function in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic graph?

Back

A vertical line that divides the graph into two mirror-image halves, given by x = -b/(2a).

Front

What does the discriminant of a quadratic equation tell you?

Back

It indicates the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.