QSE2 Review

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For the quadratic function y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -\frac{b}{2a}.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. It is given by: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

How do you determine if a quadratic equation has real solutions?

Back

To determine if a quadratic equation has real solutions, calculate the discriminant (D) using the formula D = b^2 - 4ac. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

What is the minimum value of a quadratic function?

Back

The minimum value of a quadratic function occurs at the vertex of the parabola when the coefficient of x^2 is positive. The vertex can be found using the formula x = -\frac{b}{2a}, and the minimum value can be calculated by substituting this x value back into the function.

Front

How do you find the vertex of a parabola given its equation?

Back

The vertex of a parabola given by the equation y = ax^2 + bx + c can be found using the formulas: x = -\frac{b}{2a} and y = f(-\frac{b}{2a}).

Front

What does it mean for a quadratic function to have its vertex in Quadrant 3?

Back

A quadratic function has its vertex in Quadrant 3 if both the x-coordinate and y-coordinate of the vertex are negative.

Front

Solve the quadratic equation: 2x^2 - 9x - 35 = 0 using the quadratic formula.

Back

Using the quadratic formula, the solutions are x = -5/2 and x = 7.

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant (D = b^2 - 4ac) indicates the nature of the roots of the quadratic equation. It helps determine whether the roots are real and distinct, real and equal, or complex.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them to form a parabola.