3.1-3.2 Review

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Tags

CCSS.HSG.GPE.A.1

Front

How do you determine the direction a parabola opens based on its equation?

Back

If the coefficient of the squared term is positive, the parabola opens up or right; if negative, it opens down or left.

Front

What is the focus of a parabola given in the form (y - k)² = 4p(x - h)?

Back

The focus is located at (h + p, k) for p > 0 (opens right) and (h - p, k) for p < 0 (opens left).

Front

Write the equation of a circle with center (3, -2) and radius 4.

Back

The equation is (x - 3)² + (y + 2)² = 16.

Tags

CCSS.HSG.GPE.A.1

Front

What is the vertex form of a parabola?

Back

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

Front

How do you find the radius of a circle from its equation?

Back

The radius can be found by taking the square root of the constant on the right side of the equation in standard form.

Tags

CCSS.HSG.GPE.A.1

Front

What is the relationship between the focus and directrix of a parabola?

Back

The focus is a point inside the parabola, while the directrix is a line outside the parabola; points on the parabola are equidistant from both.

Front

What does the term 'discriminant' refer to in the context of quadratic equations?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

How can you identify the center of a circle from its equation?

Back

The center (h, k) can be identified from the equation (x - h)² + (y - k)² = r².

Tags

CCSS.HSG.GPE.A.1

Front

What is the significance of the value 'p' in the parabola equation (y - k)² = 4p(x - h)?

Back

The value 'p' represents the distance from the vertex to the focus and the vertex to the directrix.