Solving Quadratics by using the Quadratic Formula

How can you rearrange the equation x² + 4x - 40 = -8 to use the Quadratic Formula?

• x² + 4x + 8 - 40 = 0, which simplifies to x² + 4x + 32 = 0.

• x² + 4x - 32 = 0, which simplifies to x² + 4x + 32 = 0.

• x² + 4x - 8 = 0, which simplifies to x² + 4x + 32 = 0.

• x² + 4x + 40 = 0, which simplifies to x² + 4x + 32 = 0.

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

• A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

• A negative discriminant indicates that the quadratic equation has one real solution.

• A negative discriminant indicates that the quadratic equation has two distinct real solutions.

• A negative discriminant indicates that the quadratic equation has infinitely many solutions.

What is the vertex of a parabola represented by a quadratic equation?

• The point where the parabola intersects the x-axis.

• The highest or lowest point of the parabola, found using the formula (-b/(2a), f(-b/(2a))).

• The point where the parabola intersects the y-axis.

• The midpoint of the line segment connecting the x-intercepts.

What does it mean for a quadratic equation to have two real solutions?

• It means that the graph of the quadratic function intersects the x-axis at two distinct points.

• It means that the quadratic function has a maximum value.

• It means that the graph of the quadratic function is a straight line.

• It means that the quadratic function has no real solutions.

What is the axis of symmetry in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

• A horizontal line that intersects the vertex of the parabola.

• The point where the parabola touches the x-axis.

• A line that passes through the focus of the parabola.

What is the role of 'a' in the Quadratic Formula?

• 'a' is the coefficient of x² and determines the shape and direction of the parabola.

• 'a' is the constant term that shifts the graph vertically.

• 'a' represents the linear coefficient that affects the slope of the parabola.

• 'a' is the variable that changes with the value of x.

What are the solutions to the equation 2x² + 7x - 15 = 0 using the Quadratic Formula?

• x = -5 and x = 1.5

• x = -3 and x = 5

• x = 2 and x = -7.5

• x = 0 and x = 7

What does it mean if the discriminant is zero?

• The quadratic equation has no real solutions.

• The quadratic equation has exactly one real solution, also known as a repeated or double root.

• The quadratic equation has two distinct real solutions.

• The quadratic equation has complex solutions.

How can you check your solutions after applying the Quadratic Formula?

• Substitute the solutions back into the original equation to verify that they satisfy the equation.

• Graph the solutions on a coordinate plane to see if they intersect the x-axis.

• Use synthetic division to confirm the solutions are correct.

• Calculate the discriminant to ensure the solutions are valid.

What are the steps to solve a quadratic equation using the Quadratic Formula?

• 1. Identify coefficients a, b, and c from the equation. 2. Calculate the discriminant (b² - 4ac). 3. Determine the number of solutions based on the discriminant. 4. Apply the Quadratic Formula to find the solutions.

• 1. Rewrite the equation in standard form. 2. Factor the quadratic expression. 3. Set each factor to zero. 4. Solve for the variable.

• 1. Identify the roots of the equation. 2. Use synthetic division to simplify. 3. Apply the quadratic formula. 4. Verify the solutions by substitution.

• 1. Graph the quadratic function. 2. Find the vertex of the parabola. 3. Determine the axis of symmetry. 4. Use the vertex to find the solutions.