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Question 1 A)Which of the following is a point you can generate to create the parabola for the quadratic equation y=−6x2+3x+8?(1 point) Responses (−6,8) left parenthesis negative 6 comma 8 right parentheis (−3,−55) left parenthesis negative 3 comma negative 55 right parentheis (−6,206) left parenthesis negative 6 comma 206 right parentheis (−3,323) left parenthesis negative 3 comma 323 right parentheis Question 2 A) Given the table of values, complete the table for the quadratic equation y=−6x2+3x+8 to find the values of the high or low point of the parabola. x y −1 −1 −0.75 2.375 −0.5 5 −0.25 0 8 0.25 8.375 0.5 0.75 1 5 Which of the following is correct? (1 point) Responses (−1,−1) is the low point on the parabola. left parenthesis negative 1 comma negative 1 right parenthesis is the low point on the parabola. (0.25,8.375) is the high point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola. (0.5,9) is the high point on the parabola. left parenthesis 0.5 comma 9 right parenthesis is the high point on the parabola. (0.25,8.375) is the low point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the low point on the parabola. Question 3 A) Use the image to answer the question. Identify one of the zeros (or x-intercepts) on the graph. (1 point) Responses (4,0) left parenthesis 4 comma 0 right parenthesis (0,2) left parenthesis 0 comma 2 right parenthesis (0,−4) left parenthesis 0 comma negative 4 right parenthesis x=1.5 x equals 1.5 Question 4 A) Use the image to answer the question. Identify the vertex on the graph. (1 point) Responses (−10,0) left parenthesis negative 10 comma 0 right parenthesis (−12,0) left parenthesis negative 12 comma 0 right parenthesis x=−11 x equals negative 11 (−11,−1) left parenthesis negative 11 comma negative 1 right parenthesis Question 5 A) Use the image to answer the question. Determine which of the following statements is true about the parabola. (1 point) Responses There is only one x-intercept. There is only one x -intercept. The vertex and the x-intercepts share the same point. The vertex and the x -intercepts share the same point. The y-intercept and the vertex share the same point. The y -intercept and the vertex share the same point. The y-intercept and the x-intercepts share the same point. The y -intercept and the x -intercepts share the same point.

1 answer

Let's address each question one by one:

Question 1 A)

To identify a point that generates the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the given x-values into the equation and see if any of the responses yield results.

  1. For \( (-6, 8) \): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad (\text{not a solution}) \]

  2. For \( (-3, -55) \): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad (\text{is a solution}) \]

  3. For \( (-6, 206) \): \[ y = -6(-6)^2 + 3(-6) + 8 = -226 \quad (\text{not a solution}) \]

  4. For \( (-3, 323) \): \[ y = -6(-3)^2 + 3(-3) + 8 = -55 \quad (\text{not a solution}) \]

Correct Response: \( (-3, -55) \) is a point that generates the parabola.

Question 2 A)

Based on the values given, we want to identify the high or low point (vertex) of the parabola represented by \( y = -6x^2 + 3x + 8 \).

From the values:

  • At \( x = -1 \), \( y = -1 \)
  • At \( x = -0.75 \), \( y = 2.375 \)
  • At \( x = -0.5 \), \( y = 5 \)
  • At \( x = -0.25 \), \( y = 8 \)
  • At \( x = 0.25 \), \( y = 8.375 \)
  • At \( x = 0.5 \), \( y = 0.75 \)
  • At \( x = 1 \), \( y = 5 \)

The highest point here is \( (0.25, 8.375) \).

Correct Response: \( (0.25, 8.375) \) is the high point on the parabola.

Question 3 A)

To identify a zero (or x-intercept) on the graph, we need points where \( y = 0 \). Among the provided options, we would typically need to examine the graph to check if any given points are x-intercepts. Given the choices, if there is a point where \( y = 0 \), it may be \( x = 1.5 \) or other options.

Without the graph, the best approach here is to point out a well-known basic property of parabolas.

If you're provided with a particular graph showing x-intercepts, you need to select the correctly identified x-intercept from there.

Question 4 A)

Again, without the image of the graph, I can't provide the exact coordinates of the vertex. If you have identified the vertex of the parabola using \( y = ax^2 + bx + c \) or interpret it from the graph, you would select the matching point among the options presented.

Typically, the vertex of a parabola described by \( ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \). Plugging the values in gives you the x-coordinate, and substituting that x back into the equation gives you the y-coordinate.

Question 5 A)

Without an image to refer to, the correct response would typically be based on the properties of the graph based on choices.

From typical properties:

  1. If the vertex is the only x-intercept, that indicates it touches the x-axis at that point.
  2. The vertex gives the highest or lowest point, depending on whether it opens upwards or downwards.

Choose the statement that best reflects the relationship depicted in the available graph.

Correct Response: Depends entirely on the graphical details provided.

If you have access to the graphs, I can help interpret them based on your observations.