Axis of Symmetry

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. It passes through the vertex.

Front

How do you find the axis of symmetry for a quadratic equation in standard form?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum point at its vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum point at its vertex.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How can you determine if a quadratic function has a maximum or minimum?

Back

You can determine this by looking at the coefficient of the x^2 term: if it's positive, the function has a minimum; if it's negative, it has a maximum.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form.

Front

What is the formula for the vertex of a parabola in vertex form?

Back

In vertex form, y = a(x-h)^2 + k, the vertex is the point (h, k).