GCSE Edexcel Maths Functions: Here is a sketch of a curve. Th

Here is a sketch of a curve - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

Question 18

Here is a sketch of a curve. The equation of the curve is $y = x^2 + ax + b$ where $a$ and $b$ are integers. The points $(0, -5)$ and $(5, 0)$ lie on the curve. F... show full transcript

Worked Solution & Example Answer:Here is a sketch of a curve - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

Step 1

Substituting the points into the curve equation

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Answer

We start by substituting the given points into the curve equation to find the values of $a$ and $b$ .

For the point $(0, -5)$ : $y = (0)^2 + a(0) + b$ Thus, we have: $-5 = b \\ b = -5$
For the point $(5, 0)$ : $y = (5)^2 + a(5) + b$ Substituting $b = -5$ : $0 = 25 + 5a - 5 \\ 0 = 20 + 5a \\ 5a = -20 \\ a = -4$

So we have found that $a = -4$ and $b = -5$ .

Step 2

Finding the turning point

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Answer

The turning point of the curve, which is a quadratic function, can be determined using the vertex form or by finding the axis of symmetry.

The x-coordinate of the turning point for $y = ax^2 + bx + c$ is given by: $x = -\frac{b}{2a}$ Substituting $a = 1$ and $b = -4$ from the equation $y = x^2 - 4x - 5$ : $x = -\frac{-4}{2 imes 1} = 2$

Now substituting $x = 2$ back into the equation to find the y-coordinate: $y = (2)^2 - 4(2) - 5 = 4 - 8 - 5 = -9$

Therefore, the coordinates of the turning point of the curve are $(2, -9)$ .

Here is a sketch of a curve - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

Worked Solution & Example Answer:Here is a sketch of a curve - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

Substituting the points into the curve equation

Finding the turning point

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