A straight line passes through the point (0, 6) and is perpendicular to y = 4x - 5 - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

To find the intersection of the two graphs, we need to set the equations equal to each other:

$4x - 5 = -x^2 - 17$

Rearranging this equation yields:

$x^2 + 4x - 12 = 0$

To solve the quadratic equation, we can factor it:

$(x + 6)(x - 2) = 0$

The solutions for x are:

$x = -6 \quad \text{or} \quad x = 2$

Now we find the corresponding y-coordinates by substituting these values back into one of the original equations, using y = 4x - 5:

For $x = -6$:

$y = 4(-6) - 5 = -24 - 5 = -29$

For $x = 2$:

$y = 4(2) - 5 = 8 - 5 = 3$

Thus, the coordinates of the intersections are:

$(-6, -29)$ and $(2, 3)$.