Answer:
Explanation:
The given equation is y - 5 = 0.5x² + 6x - 3
We have to find the number of x - intercepts the graph of this equation will make.
For x-intercepts we will put y = 0
so 0 - 5 =0.5x² + 6x - 3
0.5x² + 6x - 3 + 5 = 0
0.5x² + 6x + 2 = 0
x² + 12x + 4 = 0
We know if a quadratic equation is ax² + bx + c = 0
and b² - 4ac > 0 there will be two real roots.
In this equation b = 12, C = 4 and a = 1 (12)² - 4 × 4 = 144 - 16
= 128 > 0
Therefore, there will be two intercepts of x