GCSE OCR Maths Volume: On the same grid, draw the graph

On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Question 8

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On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$. Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$. Give your answers to 1 decim... show full transcript

Worked Solution & Example Answer:On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Step 1

Draw the graph of $y = 2x - 6$

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Answer

Identify the vertices:
- For $x = -1$ : $y = 2(-1) - 6 = -8$
- For $x = 5$ : $y = 2(5) - 6 = 4$
Plot these points on the graph: (-1, -8) and (5, 4).
Connect the points to form a straight line, ensuring it extends only between $-1$ and $5$ on the x-axis.

Step 2

Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$

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Answer

Rearrange the equation to find where the graphs intersect: $x^2 - 4x + 1 - 2x + 6 = 0$ which simplifies to: $x^2 - 6x + 7 = 0$ .
Solve for the roots using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Here, $a = 1$ , $b = -6$ , and $c = 7$ : $x = \frac{6 \pm \sqrt{(-6)^2 - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$ $= \frac{6 \pm \sqrt{36 - 28}}{2}$ $= \frac{6 \pm \sqrt{8}}{2}$ $= 3 \pm \sqrt{2}$ .
Calculate the values to 1 decimal place:
- $x \approx 3 + 1.4 = 4.4$
- $x \approx 3 - 1.4 = 1.6$

Thus, the solutions are: $x \approx 4.4 \text{ or } 1.6$ .

On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Worked Solution & Example Answer:On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Draw the graph of $y = 2x - 6$

Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$

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