Graphing Quadratics Remediation

Front

What is the axis of symmetry in a quadratic equation?

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) for a quadratic equation in the form y = ax^2 + bx + c.

Front

How do you find the vertex of a parabola given in vertex form?

Back

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

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum value at its vertex, and the coefficient 'a' in the equation y = ax^2 + bx + c is positive.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum value at its vertex, and the coefficient 'a' in the equation y = ax^2 + bx + c is negative.

Front

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

Back

You can determine this by looking at the sign of the coefficient 'a' in the quadratic equation. If 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you convert from standard form to vertex form?

Back

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

Front

What is the significance of the y-intercept in 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 x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x.

Front

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

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the original quadratic function.