Question

block: 5th date: 11. which of these quadratic functions is shown in the graph? a. $y = (x + 3)^2 + 1$ b. $y = (x - 3)^2 - 1$ c. $y = (x + 3)^2 - 1$ d. $y = (x - 3)^2 + 1$ 12 what is the equation for the axis of symmetry? a. $x = -3$ b. $x = 3$ c. $y = 1$ d. $y = -1$ →use the graph shown to answer questions 11 and 12 13. which of these quadratic function is shown in the graph? a. $y = -(x + 5)^2 + 4$ b. $y = (x + 5)^2 + 4$ c. $y = -(x + 4)^2 + 5$ d. $y = (x + 4)^2 + 5$ 14. list all the ways that the graph of the parent function $y = x^2$ would be transformed to create the graph of the new function $y = -(x - 1)^2 - 5$. a. translated right 1 and down 5 only b. translated right 1 and down 5, vertically stretched (thinner shape) c. translated right 1 and down 5, vertically shrunk (wider shape) d. translated right 1 and down 5, reflected (opens down)

Explanation:

Question 11

Step1: Recall vertex form of quadratic

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

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the minimum point) is at \((3, -1)\). So \( h = 3 \) and \( k = -1 \).

Step3: Substitute h and k into vertex form

Substituting \( h = 3 \) and \( k = -1 \) into \( y = (x - h)^2 + k \), we get \( y = (x - 3)^2 - 1 \).

Step1: Recall axis of symmetry formula

For a quadratic function in vertex form \( y = (x - h)^2 + k \), the axis of symmetry is the vertical line \( x = h \).

Step2: Determine h from the vertex

From the graph, the vertex is at \((3, -1)\), so \( h = 3 \). Thus, the axis of symmetry is \( x = 3 \).

Step1: Recall vertex form and direction

The vertex form is \( y = a(x - h)^2 + k \). If \( a < 0 \), the parabola opens downward. From the graph, the parabola opens downward, so \( a = -1 \).

Step2: Identify the vertex

Looking at the graph (despite the noise), the vertex seems to be at \((-4, 5)\) (since the options have \( x + 4 \) which is \( x - (-4) \) and \( +5 \) for \( k \)).

Step3: Substitute into vertex form

With \( a = -1 \), \( h = -4 \), \( k = 5 \), the equation is \( y = - (x + 4)^2 + 5 \).

Answer:

B. \( y = (x - 3)^2 - 1 \)

Question 12