Graphing Quadratics

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

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

Back

If the coefficient of the x^2 term (a) is positive, the parabola opens upwards. If it is negative, the parabola opens downwards.

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. It can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax^2 + bx + c.

Front

What are the coefficients a, b, and c in the quadratic equation ax^2 + bx + c?

Back

In the quadratic equation ax^2 + bx + c, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0. This gives the point (0, c) where c is the constant term.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How can you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (ax^2 + bx + c) to vertex form (a(x-h)^2 + k), you can complete the square.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does it mean for a quadratic function to be in factored form?

Back

A quadratic function is in factored form when it is expressed as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.