Vertex Form Quadratics

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex of the parabola.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

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

Back

To convert from standard form (y = ax² + bx + c) to vertex form, you can complete the square.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How do you find the y-intercept from the equation f(x) = ax² + bx + c?

Back

The y-intercept can be found by substituting x = 0 into the equation, resulting in the point (0, c).

Front

What is the relationship between the roots of a quadratic equation and its axis of symmetry?

Back

The axis of symmetry is located exactly halfway between the two roots of the quadratic equation.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How do you determine the roots of a quadratic equation from its vertex form?

Back

To find the roots from vertex form, set y = 0 and solve for x using the equation y = a(x - h)² + k.

Front

What does the vertex of a parabola represent?

Back

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