Escribe funciones cuadráticas a partir de puntos

What is the vertex form of a quadratic function?

• y = a(x-h)^2 - k

• y = a(x-h)^2 + k

• y = a(x+h)^2 + k

• y = a(x+h)^2 - k

If the vertex of a quadratic function is (3, 4) and it passes through the point (6, 10), what is the equation of the function?

• y = 2(x-3)^2 + 4

• y = 3(x-3)^2 + 4

• y = 1/2(x-5)^2 + 10

• y = 1/2(x-3)^2 + 4

What is the formula to find the vertex of a quadratic function?

• x = -b / (2c)

• x = a / (2b)

• x = -a / (2b)

• x = -b / (2a)

Explain the process of converting a quadratic function from standard form to vertex form.

• Complete the square by halving the coefficient of the linear term, squaring it, and adding/subtracting it appropriately to get the vertex form.

• Ignore the linear term and directly write the quadratic term in vertex form.

• Divide the quadratic term by the linear term to convert to vertex form.

• Multiply the linear term by the constant term and add/subtract it to get the vertex form.

If a quadratic function has a vertex at (-2, 5) and passes through the point (0, 1), what is the equation of the function?

• y = -1(x - 2)^2 + 5

• y = -2(x + 2)^2 - 5

• y = 2(x + 2)^2 + 5

• y = -1(x + 2)^2 + 5

What is the significance of the vertex in a quadratic function?

• The vertex is the x-intercept of the parabola.

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

• The vertex is the point where the parabola changes direction.

• The vertex is the maximum or minimum point of the parabola.

If a quadratic function has a vertex at (1, -3) and passes through the point (2, 0), what is the equation of the function?

• y = 3(x-1)^2 - 3

• y = 3(x-1)^2 + 3

• y = 2(x-1)^2 - 3

• y = 3(x-2)^2 - 3

How do you determine the direction of opening of a quadratic function based on its equation?

• Look at the constant term. If positive, opens upwards. If negative, opens downwards.

• Look at the coefficient of the squared term. If positive, opens upwards. If negative, opens downwards.

• The number of x-intercepts determines the direction of opening.

• The leading coefficient determines the direction of opening.

Solve for x:

x² - 9x + 20 = 0

• x = -4 and x = -5
• x = 20 and x = -9
• x = 4 and x = 5
• x = -4 and x = 5

2d² = 8

• 4
• -2
• -4, 4
• -2, 2