Solve a Quadratic by Graphing

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to solve a quadratic by graphing?

Back

Solving a quadratic by graphing involves plotting the quadratic function on a coordinate plane and identifying the points where the graph intersects the x-axis, which represent the solutions.

Front

What are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called zeros, roots, or x-intercepts.

Front

How many solutions can a quadratic equation have?

Back

A quadratic equation can have 0, 1, or 2 solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

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, passing through the vertex.

Front

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

Back

The discriminant (b² - 4ac) determines the number of solutions: if it's positive, there are 2 solutions; if it's zero, there is 1 solution; if it's negative, there are no real solutions.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, corresponding to the solutions of the equation.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.