Completing The Square Practice

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

• The coefficients a, b, and c affect the width, direction, and position of the parabola on the graph.

• The coefficients determine the number of roots the equation has.

• The coefficients only affect the position of the vertex of the parabola.

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

How can you identify the axis of symmetry for a quadratic function?

• x = -b/(2a)

• x = b/(2a)

• x = -c/(2a)

• x = c/(2b)

What is the role of the 'a' coefficient in a quadratic equation?

• The 'a' coefficient determines the direction and width of the parabola: larger |a| values make the parabola narrower.

• The 'a' coefficient affects the color of the graph.

• The 'a' coefficient indicates the number of solutions to the equation.

• The 'a' coefficient represents the y-intercept of the parabola.

What is the value of 'c' that completes the square in the expression x^2 + 28x + c?

• 196

• 144

• 100

• 256

What is the quadratic formula used to find the roots of a quadratic equation?

• n = (-b ± √(b² - 4ac)) / (2a)

• n = (b ± √(b² + 4ac)) / (2a)

• n = (-b ± √(b² + 4ac)) / (2a)

• n = (b ± √(b² - 4ac)) / (2a)

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

• By factoring the quadratic expression.

• By completing the square on the quadratic expression.

• By using the quadratic formula to find the roots.

• By graphing the equation and identifying the vertex.

What is the general shape of a quadratic function's graph?

• A straight line

• A circle

• A parabola

• An ellipse

How do you find the y-intercept of a quadratic function?

• By evaluating the function at x = 0, which gives y = c.

• By finding the vertex of the parabola.

• By solving the equation for x when y = 0.

• By using the quadratic formula to find the roots.

How do you complete the square for the expression x^2 + bx?

• Add (b/2)^2 to the expression: x^2 + bx + (b/2)^2.

• Multiply the expression by 2: 2x^2 + 2bx.

• Subtract (b/2)^2 from the expression: x^2 + bx - (b/2)^2.

• Factor the expression: (x + b/2)^2.

What is the standard form of a quadratic equation?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = mx + b

• y = a(x + b)(x + c)