The graph of the quadratic function f in the xy-plane is a parabola with vertex (3, 12). I… — SAT

The graph of the quadratic function $f$ in the $xy$ -plane is a parabola with vertex $(3, 12)$ . If the graph passes through the point $(5, 8)$ , what is the $y$ -value of the point on the graph where $x = 1$ ?

Cevap: 8

Cevap

The correct answer is

8

The vertex of the parabola is given as

(3, 12)

, which means the axis of symmetry is the line

x = 3

. Since a parabola is symmetric with respect to its axis of symmetry, any two points on the parabola that are equidistant from this line must share the same

y

-coordinate. The given point has an

x

-coordinate of

5

, which is

5 - 3 = 2

units to the right of the axis of symmetry. The target point has an

x

-coordinate of

1

, which is

3 - 1 = 2

units to the left of the axis of symmetry. Because both points are exactly

2

units away from the axis of symmetry, their

y

-coordinates are equal. Therefore, the

y

-value of the point where

x = 1

8

Adım Adım Çözüm

Determine the axis of symmetry of the parabola.

The axis of symmetry is the vertical line

x = 3

The vertex of a parabola

(h, k)

always lies on its axis of symmetry, which is

x = h

Find the horizontal distance from the axis of symmetry to the given point.

The distance from

x = 3

x = 5

|5 - 3| = 2

units.

This measures how far the point is horizontally from the line of symmetry.

Find the horizontal distance from the axis of symmetry to the target point.

The distance from

x = 3

x = 1

|1 - 3| = 2

units.

This determines if the target point is symmetric to the given point.

Equate the y-values using symmetry.

The

y

-value at

x = 1

8

Because both

x = 5

and

x = 1

are

2

units away from the axis of symmetry, their corresponding

y

-values must be identical.

Anahtar Kavram

Symmetry of Quadratic Graphs

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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