Matching Graphs to Standard, Vertex, Factored Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex form of a quadratic equation look like?

Back

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

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is written as y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the equation.

Front

How can you identify the vertex of a parabola from its vertex form?

Back

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

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction and width of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.

Front

What is the relationship between the roots and the factored form of a quadratic equation?

Back

The roots of the quadratic equation are the values of x that make the equation equal to zero, represented in factored form as y = a(x - r₁)(x - r₂).

Front

How can you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What does it mean for a parabola to be 'narrow' or 'wide'?

Back

A 'narrow' parabola has a larger absolute value of 'a' (|a| > 1), while a 'wide' parabola has a smaller absolute value of 'a' (|a| < 1).

Front

What is the y-intercept of a quadratic equation in standard form?

Back

The y-intercept is the value of c in the standard form y = ax² + bx + c, which is the point where the graph crosses the y-axis.