Find the x‑intercepts. Show complete working, a. y = 4x2 + 20x + 9b. y = 8x2 − 6x

a. y = 4x^2 + 20x + 9

To find the x-intercepts, we set y = 0 and solve for x.

0 = 4x^2 + 20x + 9

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Here, we'll use the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / (2a)

where a = 4, b = 20, and c = 9.

x = [-20 ± sqrt((20)^2 - 449)] / (2*4) x = [-20 ± sqrt(400 - 144)] / 8 x = [-20 ± sqrt(256)] / 8 x = [-20 ± 16] / 8 x = -4, -1

So, the x-intercepts are x = -4 and x = -1.

b. y = 8x^2 - 6x

Again, to find the x-intercepts, we set y = 0 and solve for x.

0 = 8x^2 - 6x

We can factor out an x from each term:

0 = x(8x - 6)

Setting each factor equal to zero gives the solutions x = 0 and x = 6/8 = 0.75.

So, the x-intercepts are x = 0 and x = 0.75.