Question

The number of x-intercepts for the following quadratic functions are

i) y=-3(x – 4)2 + 5
ii) y = (x + 3)
iii) y = 4(x - 2)2 + 5

Answer 1

The number of x-intercepts for the given quadratic functions are explained.

Step-by-step explanation:

For the quadratic function y=-3(x – 4)2 + 5, the vertex form of the equation is y=a(x-h)2+k, where (h, k) is the vertex of the parabola. In this case, the vertex is (4, 5). Since the parabola opens downwards, there are no x-intercepts.

For the quadratic function y = (x + 3), the equation is already in standard form. Since this is a linear equation, there is exactly one x-intercept when y = 0, which is x = -3.

For the quadratic function y = 4(x - 2)2 + 5, the vertex form of the equation is y=a(x-h)2+k. In this case, the vertex is (2, 5). Since the parabola opens upwards, there are no x-intercepts.