Alg Quadratic Applications

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

To find the maximum height, use the formula x = -b/(2a) to find the time at which the maximum occurs, then substitute this value back into the height equation.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if its graph intersects the x-axis, which occurs when the discriminant (b² - 4ac) is greater than or equal to zero.

Front

How can you determine when an object will hit the ground using a quadratic equation?

Back

Set the height equation equal to zero and solve for t to find when the object reaches a height of 0.

Front

What is the formula for the height of an object in free fall?

Back

The height h(t) of an object in free fall can be modeled by h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

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, given by the formula x = -b/(2a).

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form ax² + bx + c.