Everything Maths Grade 10

6.7 Interpretation of graphs EMA5J

Worked example 22: Determining the equation of a parabola

QUESTION

Use the sketch below to determine the values ofaandqfor the parabola of the formy=ax^2 +q.

(1; 0)^0

(0; 1)

x

y

SOLUTION

Step 1: Examine the sketch

From the sketch we see that the shape of the graph is a “frown”, thereforea < 0. We also see that the graph

has been shifted vertically upwards, thereforeq > 0.

Step 2: Determinequsing they-intercept

They-intercept is the point(0; 1).

y=ax^2 +q

1 =a(0)^2 +q

)q= 1

Step 3: Use the other given point to determinea

Substitute point(1; 0)into the equation:

y=ax^2 +q

0 =a(1)^2 + 1

)a= 1

Step 4: Write the final answer

a= 1 andq= 1, so the equation of the parabola isy=x^2 + 1.

208 6.7. Interpretation of graphs