MIXED PRACTICE- SOLVING QUADRATICS (ALL METHODS)

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

The quadratic formula is given by x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} for a quadratic equation in the form ax^2 + bx + c = 0.

Front

What are the roots of the equation (x - 3)(x + 6) = 0?

Back

The roots are x = 3 and x = -6.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, which can be found using x = -\frac{b}{2a}.

Front

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

Back

The discriminant, given by D = b^2 - 4ac, determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you find the height of an object modeled by a quadratic function?

Back

Substitute the time value into the quadratic function to find the height at that specific time.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you solve the quadratic equation x^2 + 2x - 24 = 0?

Back

Factoring gives (x + 6)(x - 4) = 0, so the solutions are x = -6 and x = 4.

Front

What is the height of a baseball after 2 seconds if its height is modeled by h(t) = -16t^2 + 72t + 15?

Back

Substituting t = 2 gives h(2) = -16(2)^2 + 72(2) + 15 = 95 feet.