After 10.2 Quadratic Key Features Flashcard

Front

What is the formula to find the axis of symmetry for a quadratic equation?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation in the form y = ax^2 + bx + c.

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0. This gives the point (0, c) where c is the constant term in the equation y = ax^2 + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function has a maximum value?

Back

If a quadratic function has a maximum value, it means the parabola opens downwards, and the vertex of the parabola is the highest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What is another term for the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are also known as the roots or solutions of the equation.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the number of solutions (roots) a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (D = b^2 - 4ac). If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the parabola changes direction. It can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The maximum or minimum value of a quadratic function can be found at the vertex, using the formula k = f(h) where h = -b/(2a).

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7A

Front

What is the relationship between the roots and the factors of a quadratic equation?

Back

The roots of a quadratic equation correspond to the values of x that make the equation equal to zero, and they can be expressed as factors in the form y = a(x - r1)(x - r2) where r1 and r2 are the roots.

Tags

CCSS.HSF-IF.C.7C