Question

By completing the square, find the coordinates of the turning point of the curve with the equation y = x² + 8x + 3 You must show all your working.

Answer 1

To find the turning point of the given quadratic curve y = x² + 8x + 3, complete the square to rewrite the equation in vertex form. The resulting vertex form is y = (x + 4)² - 13, revealing the turning point's coordinates to be (-4, -13).

Step-by-step explanation:

The curve you have provided is y = x² + 8x + 3. To find the turning point, we can complete the square. The general form for completing the square is (x + h)² = y + k where (h, k) is the vertex of the parabola. Here's how to complete the square for the given quadratic equation:

• Group the x terms: y = (x² + 8x) + 3.
• Determine the value that completes the square for the x terms: (8/2)² = 16.
• Add and subtract this value inside the parenthesis: y = (x² + 8x + 16 - 16) + 3.
• Rewrite the equation with a perfect square trinomial: y = ((x + 4)² - 16) + 3.
• Simplify the equation: y = (x + 4)² - 13.

Now, the vertex form of the quadratic equation is y = (x + 4)² - 13. Therefore, the coordinates of the turning point, which is the vertex of the parabola, are (-4, -13).

Answer 2

Step-by-step explanation:

Write properties of function:

vertex form:

vertex form:

vertex:

vertex:

EXPLANATION

Write properties of function: Write properties of function:

vertex form: y = (x + 4)^{2} - 13

vertex form: y = (x + 4)^{2} - 13

vertex: (-4,-13)

vertex: (-4,-13)

Answer: Write properties of function:

vertex form: y = (x + 4)^{2} - 13

vertex form: y = (x + 4)^{2} - 13

vertex: (-4,-13)

vertex: (-4,-13)

Write properties of function: Write properties of function:

vertex form:

vertex form:

vertex:

vertex:

Answer: Write properties of function:

vertex form:

vertex form:

vertex:

vertex: