Coll Alg Unit 4 WU

Front

What is the vertex of a parabola?

Back

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

Front

How do you determine if a vertex is a maximum or minimum?

Back

If the parabola opens upwards, the vertex is a minimum. If it opens downwards, the vertex is a maximum.

Front

What is the y-intercept of a quadratic equation?

Back

The y-intercept is the point where the graph intersects the y-axis, found by setting x=0 in the equation.

Front

How do you find the direction a parabola opens?

Back

The direction can be determined by the coefficient of the x^2 term: if it's positive, the parabola opens up; if negative, it opens down.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you find the x-intercepts of a quadratic equation?

Back

Set y=0 and solve the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).

Front

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

Back

Use the method of completing the square to rewrite the equation in the form y = a(x-h)² + k, where (h,k) is the vertex.