GCSE Secondary Maths Age 13-17 - Graphs: Graphs - Explained

The video tutorial explains how to analyze a parabola graphically, solve equations using graphs, and estimate the gradient of a curve at a specific point. It begins with an introduction to the parabola and its properties, followed by a demonstration of solving equations graphically by drawing suitable lines. The tutorial then covers how to estimate the gradient of a curve at a point by drawing a tangent. The video concludes with reflections on the difficulty of the tasks and advice for students to practice these skills.

What is the y-intercept of the parabola y = x^2 - 2x + 3?

• 3

• 2

• 4

• 1

Why is the parabola y = x^2 - 2x + 3 considered upright?

• The x-intercept is positive

• The y-intercept is positive

• The coefficient of x^2 is positive

• The coefficient of x is positive

What is the purpose of drawing a straight line on the graph of y = x^2 - 2x + 3?

• To find the x-intercepts

• To find the y-intercepts

• To calculate the gradient

• To estimate solutions for x^2 - 3x - 1 = 0

What equation is used to find the intersection points with the parabola?

• y = x^2 - 2x + 3

• y = 2x + 4

• y = x + 4

• y = x^2 - 3x - 1

What is the gradient of the line y = x + 4?

• 3

• 2

• 1

• 0

How do you find the gradient of a curve at a specific point?

• By finding the y-intercept

• By finding the x-intercept

• By drawing a tangent line

• By drawing a perpendicular line

What is the formula for calculating the gradient of a line?

• Difference of x and y

• Change in y over change in x

• Change in x over change in y

• Sum of x and y

What is the estimated gradient of the tangent at point P?

• 2.5

• 1.5

• 2.0

• 1.9

What range of values is acceptable for the gradient of the tangent at point P?

• 1.0 to 2.0

• 1.6 to 2.5

• 2.0 to 3.0

• 1.5 to 2.0

What is emphasized as crucial for improving skills in solving these types of questions?

• Discussion

• Memorization

• Practice

• Guesswork