Question

Find the x- and y-intercept of the parabola y = x² + 4x + 2

Answer 1

Answer:

x-intercept = (- 2 + √2, 0) (- 2 - √2, 0)

y-intercept = (2, 0)

Step-by-step explanation:

Given expression

y = x² + 4x + 2

Find the x-intercept

Definition of x-intercept is the point that intersects with the x-axis, which means the y value is 0

(0) = x² + 4x + 2

(x + 2 - √2) (x + 2 + √2) = 0

x = -2 ± √2

Therefore, the x-intercepts are $\Large\boxed{(-2+\sqrt{2},~0) }$ $\Large\boxed{(-2-\sqrt{2},~0) }$

Find the y-intercept

Definition of x-intercept is the point that intersects with the y-axis, which means the x value is 0

y = (0)² + 4(0) + 2

y = 0 + 0 + 2

y = 2

Therefore, the y-intercept is $\Large\boxed{(0,~2)}$

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