The graph of $y = 2x^2 + 3x - 9$ is drawn below. (a) Use the graph to solve $2x^2 + 3x - 9 = 0$. (b) The equation $2x^2 + x - 4 = 0$ can be solved by finding the intersection of the graph of $y = 2x^2 + 3x - 9$ and the line $y = ax + b$. (i) Find the value of a and the value of b. (ii) Hence use the graph to solve the equation $2x^2 + x - 4 = 0$.

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The graph of $y = 2x^2 + 3x - 9$ is drawn below - OCR - GCSE Maths - Question 19 - 2020 - Paper 6

Question 19

The graph of $y = 2x^2 + 3x - 9$ is drawn below. (a) Use the graph to solve $2x^2 + 3x - 9 = 0$. (b) The equation $2x^2 + x - 4 = 0$ can be solved by finding the i... show full transcript

Worked Solution & Example Answer:The graph of $y = 2x^2 + 3x - 9$ is drawn below - OCR - GCSE Maths - Question 19 - 2020 - Paper 6

Step 1

Use the graph to solve $2x^2 + 3x - 9 = 0$.

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Answer

To solve the equation $2x^2 + 3x - 9 = 0$ using the graph, identify the points where the curve intersects the x-axis. From the graph, we observe that the curve intersects the x-axis at two points: approximately $x = -3$ and $x = 1$ . Hence, the solutions are:

$x = -3$ or $x = 1$ .

Step 2

Find the value of a and the value of b.

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Answer

To find the values of $a$ and $b$ , we need to determine the slope and y-intercept of the line $y = ax + b$ that intersects the curve $y = 2x^2 + 3x - 9$ at a specific point. Observing the graph, choose a point of intersection, for example, $(-1, -8)$ . The slope of the line $a$ can be calculated as follows:

Calculate the change in $y$ over the change in $x$ using another point on the curve, for example, $(0, -9)$ : $a = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-8)}{0 - (-1)} = \frac{-1}{1} = -1$
The y-intercept $b$ can be determined from the equation $y = ax + b$ : $-8 = -1(-1) + b \Rightarrow b = -8 + 1 = -7$ Thus, $a = -1$ and $b = -7$ .

Step 3

Hence use the graph to solve the equation $2x^2 + x - 4 = 0$.

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Answer

To solve the equation $2x^2 + x - 4 = 0$ using the graph, we will plot the line $y = -1x - 7$ . The $y$ value of this line at the points where it intersects the curve $y = 2x^2 + 3x - 9$ helps us find the solutions: Observe where the line intersects the curve. From the graph, the intersection points occur at approximately:

$x = -2$ and $x = 3$ . Thus, the solutions are:

$x = -2$ or $x = 3$ .

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The graph of $y = 2x^2 + 3x - 9$ is drawn below - OCR - GCSE Maths - Question 19 - 2020 - Paper 6

Worked Solution & Example Answer:The graph of $y = 2x^2 + 3x - 9$ is drawn below - OCR - GCSE Maths - Question 19 - 2020 - Paper 6

Use the graph to solve $2x^2 + 3x - 9 = 0$.

Find the value of a and the value of b.

Hence use the graph to solve the equation $2x^2 + x - 4 = 0$.

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