Completing the Square Practice

What is the relationship between the coefficients of a quadratic equation and its graph?

• The coefficients determine the shape, direction, and position of the parabola on the graph.

• The coefficients only affect the width of the parabola.

• The coefficients have no effect on the graph of the quadratic equation.

• The coefficients determine the color of the graph.

What is the vertex form of a quadratic equation?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

• y = a(x - h)^2 - k

What is the process of completing the square?

• A method used to solve linear equations by factoring them.

• A technique for rewriting quadratic equations as perfect square trinomials.

• A way to graph quadratic functions by finding their vertex.

• A strategy for simplifying polynomial expressions.

What is the significance of the discriminant in a quadratic equation?

• It determines the coefficients of the equation.

• It indicates the number of solutions: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

• It provides the vertex of the parabola.

• It calculates the area under the curve.

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

• Complete the square on the quadratic expression and rewrite the equation in the form @@y = a(x - h)^2 + k@@.

• Factor the quadratic expression and find the roots.

• Use the quadratic formula to find the vertex.

• Graph the equation and identify the vertex.

Solve the equation @@x^2 - 4x + 4 = 20@@ by completing the square.

• @@(x - 2)^2 = 20@@

• @@(x - 4)^2 = 20@@

• @@(x + 2)^2 = 20@@

• @@(x - 2)^2 = 16@@

What is a perfect square trinomial?

• An expression that can be factored into the square of a binomial, typically in the form of @@ (a + b)^2 = a^2 + 2ab + b^2 @@.

• A polynomial that has three terms and cannot be factored.

• A quadratic equation that has two distinct real roots.

• An expression that is always positive regardless of the value of the variable.

What is the formula for solving quadratic equations using the quadratic formula?

• @@x = rac{-b \pm \\sqrt{b^2 - 4ac}}{2a}@@

• @@x = rac{-b \\pm \\sqrt{b^2 + 4ac}}{2a}@@

• @@x = rac{-b \\pm \\sqrt{4ac - b^2}}{2a}@@

• @@x = rac{b \\pm \\sqrt{b^2 - 4ac}}{2a}@@

How do you find the vertex of a parabola given in standard form @@y = ax^2 + bx + c@@?

• Use the formula @@h = -\frac{b}{2a}@@ and substitute back to find @@k@@.

• Calculate the roots of the equation using the quadratic formula.

• Graph the parabola and identify the highest or lowest point.

• Use the formula for the slope of the parabola to find the vertex.

What is the role of the constant term in a quadratic equation when completing the square?

• The constant term is adjusted to create a perfect square trinomial, which simplifies solving the equation.

• The constant term is ignored and does not affect the equation.

• The constant term is used to determine the vertex of the parabola.

• The constant term is replaced with the leading coefficient.