Answer:
x-intercepts: (-1, 0) and (2, 0)
x-intercept: (-3, 0)
Step-by-step explanation:
Given <u>quadratic function</u>:
The <u>x-intercepts</u> of a <u>quadratic function</u> are the points at which the curve <u>crosses the x-axis</u> ⇒ when y = 0
Therefore, to find the x-intercepts of the given function, set the function to zero:
Factor out -4:
Divide both sides by -4
Rewrite the middle term as -2x + x:
Factor the first two terms and the last two terms separately:
Factor out the common term (x - 2):
<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):
Therefore, the x-intercepts are (-1, 0) and (2, 0).
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Given <u>quadratic equation</u>:
Add 9 to both sides:
Rewrite the middle term as 3x + 3x:
Factor the first two terms and the last two terms separately:
Factor out the common term (x + 3):
Square root both sides:
Solve for x:
Therefore, the x-intercept is (-3, 0).
As the function has a <u>repeated factor</u> (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.