Intro to Quadratic Equations

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 is the standard form of a quadratic function?

Back

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

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a U-shaped curve called a parabola.

Front

What is the vertex of a parabola?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0) = c.