Question

Mark for review
Q 61 Determine the number of intercepts with
x-axis of the parabola defined by
equation x2 - 7x + 8.
​

Answer 1

Parabola

To find: The number of intercepts with x- axis of the parabola (x² - 7x + 8).

Solution:

Let, y = x² - 7x + 8

This is the parabola which opens above.

To find intersection by x- axis, we put y = 0.

This gives: x² - 7x + 8 = 0

Now the value of the discriminant is

D = (- 7)² - 4 * 1 * 8

= 49 - 32

= 17 > 0, and thus we can conclude that the equation gives positive values of x.

Therefore the parabola intersects the x- axis at two points.

Number of intercepts = 2.

Note: To find the points of intersection, solve the equation using quadratic formula or use square method.

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