Question

What are the features of the quadratic function ƒ(x) = (x – 3)(x + 7)?

Question 8 options:


A)


Vertex = (2,25), y-intercept = (0,21), x-intercepts = (7,0) and (–3,0), axis of symmetry is x = 2


B)


Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = 2


C)


Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2


D)


Vertex = (–2,25), y-intercept = (0,21), x-intercepts = (7,0) and (3,0), axis of symmetry is x = –2

Answer 1

Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2

Explanation:

Answer 2

Option C:Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2

Explanation:

We are given the function;

f(x) = (x - 3)(x + 7)

The axis of symmetry in a quadratic equation is given by the formula;

x = -b/2a

Expanding the function given, we have;

f(x) = x² + 4x - 21

a = 1

b = 4

c = - 21

Thus;

Axis of symmetry is:

x = -(4)/(2 × 1)

x = -2

Now, y-intercept is when x = 0

Thus;

f(0) = (0 - 3)(0 + 7)

f(0) = - 3 × 7 = - 21

y - intercept is (0, - 21)

x-intercept is when f(x) = 0

Thus;

(x - 3)(x + 7) = 0

Thus;

x - 3 = 0 or x + 7 = 0

x = 3 or x = - 7

x - intercept is (-7, 0) and (3,0)

The y-coordinate of vertex will be at the line of axis of symmetry.

Thus, we will put x = -2 into the function to get;

y = (-2 - 3)(-2 + 7)

y = -5 × 5 = - 25

Vertex is at (-2, -25)

Correct Answer is option C