y - 5 = 0.5x2 + 6x - 3 How many x-intercepts does the graph of this quadratic have? Two x-intercepts One x-intercept No x-intercepts

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Step-by-step 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