Apply your understanding of quadratic functions and transformations, and sketch:

𝑦
=
0.25
(
𝑥
+
6
)
2
−
4

In this quiz, type the y-intercept in the box.

AND

Sketch on paper. Label the vertex and the intercepts, with their coordinates.

(Answer in quiz: 1 mark)
(Written answer: 2 marks)

Question

Apply your understanding of quadratic functions and transformations, and sketch:

𝑦
=
0.25
(
𝑥
+
6
)
2
−
4

In this quiz, type the y-intercept in the box.

AND

Sketch on paper. Label the vertex and the intercepts, with their coordinates.

(Answer in quiz: 1 mark)
(Written answer: 2 marks)

BlackTom AI · Accepted Answer

The problem asks to apply understanding of quadratic functions and transformations and to find the y-intercept of the function y = 0.25(x + 6)^2 − 4.
First, recall that the y-intercept occurs where x = 0, since the y-intercept is the point where the graph crosses the y-axis.
Plugging x = 0 into the function gives y = 0.25(0 + 6)^2 − 4 = 0.25 * 36 − 4.
Compute 0.25 * 36 carefully: 36 divided by 4 is 9, so 0.25 * 36 = 9.
Then subtract 4: 9 − 4 = 5.
Therefore, the y-intercept is at the point (0, 5), so the y-intercept value is 5.
Now, compare this to the provided answer: -0.5. This value does not match the calculation above, and it does not correspond to the y-intercept of the given quadratic. It would be inconsistent with evaluating the function at x = 0.
Additionally, you can verify by considering the vertex form: since the vertex is at (-6, −4) and the parabola opens upward (coefficient 0.25 > 0), the y-value at x = 0 should be above −4, which 5 clearly is. A quick sanity check confirms that the y-value increases from the vertex as x moves toward 0, consistent with obtaining y = 5 at x = 0.
If a student is asked to sketch and label the vertex and intercepts, you would place the vertex at (−6, −4), the y-intercept at (0, 5), and the x-intercepts where y = 0 would be found by solving 0.25(x + 6)^2 − 4 = 0, giving (x + 6)^2 = 16, so x = −2 or x = −10, i.e., x-intercepts at (−2, 0) and (−10, 0).
Since the question indicates to provide the y-intercept in the box and there is no multiple-choice set to evaluate, the essential result to report is y-intercept = 5, not −0.5.

Apply your understanding of quadratic functions and transformations, and sketch: 𝑦 = 0.25 ( 𝑥 + 6 ) 2 − 4 In this quiz, type the y-intercept in the box. AND Sketch on paper. Label the vertex and the intercepts, with their coordinates. (Answer in quiz: 1 mark) (Written answer: 2 marks)

View Explanation

Log in for full answers

Similar Questions

Quadratic Function For the function defined by , find the following values. Simply your answers. [Fill in the blank] [Fill in the blank] [Fill in the blank] [Fill in the blank]

Let be a quadratic function. Suppose we have given the following information: and . Which of the following answers are correct (Please note that exactly two are correct). If you cannot find the formula of the function, you still can find the shape of its graph by using a graphical argument.

An equation of the graph shown could be:

The graph of [math: y] versus [math: x2] x^2 is shown. The rule connecting [math: y] and [math: x] is :

MTH1010_05_10_4

MTH1010_05_04_1

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler