Quadratic simultaneous equations practice questions with answers

Answer: (-1, 5) and (1, 5)

1. x^2+4=5.
2. x^2=1.

• Method (1): x^2+4=5.
• Accuracy (1): Answer (-1, 5) and (1, 5)

Answer: (1, 1) and (3, 9)

1. x^2-4x+3=0.
2. (x-1)(x-3)=0.

• Method (1): x^2-4x+3=0.
• Accuracy (1): Answer (1, 1) and (3, 9)

Answer: (-1, 4) and (2, 7)

1. x^2-x-2=0.
2. (x-2)(x+1)=0, then use the line for y.

• Method (1): x^2-x-2=0.
• Accuracy (1): Answer (-1, 4) and (2, 7)

Answer: one

1. x^2-2x+1=0.
2. This is a repeated root, so the line is a tangent.

• Method (1): x^2-2x+1=0.
• Accuracy (1): Answer one

Answer: y=2x-1

1. Discriminant of x^2-2x+1 is 0.
2. x^2-2x and x^2-2x-1 are not zero discriminants.

• Method (1): Discriminant of x^2-2x+1 is 0.
• Accuracy (1): Answer y=2x-1

Answer: y=x+6

1. y values are 4 and 9.
2. Gradient (9-4)/(3-(-2))=1, so y-4=1(x+2).

• Method (1): y values are 4 and 9.
• Accuracy (1): Answer y=x+6

Answer: (-2, 4) and (3, 9)

1. x^2-x-6=0.
2. (x-3)(x+2)=0.
3. Points (-2, 4) and (3, 9).

• Method (1): Substitute
• Method (1): Factor
• Accuracy (1): First point
• Accuracy (1): Second point

You then have one equation in x, so the meetings can be solved. You then have one equation in x, so the meetings can be solved.

The line cuts the parabola at two points. The line cuts the parabola at two points.

The line is a tangent. It touches the curve once. The line is a tangent. It touches the curve once.

The line misses the curve. There is no intersection. The line misses the curve. There is no intersection.

Each intersection is a coordinate pair. You still need y. Each intersection is a coordinate pair. You still need y.

The line is usually quicker. The curve must give the same y. The line is usually quicker. The curve must give the same y.

Both points also satisfy y=x^2, so they lie on both graphs. Both points also satisfy y=x^2, so they lie on both graphs.

Adding is for two linear equations. Here one equation is quadratic, so you substitute. Adding is for two linear equations. Here one equation is quadratic, so you substitute.

The y-values are 1 and 9, so the gradient is 4. The y-values are 1 and 9, so the gradient is 4.

Yes, if it sits above the turning point. y=5 meets it at two points. Yes, if it sits above the turning point. y=5 meets it at two points.

Yes. y=0 touches the parabola at the origin. Yes. y=0 touches the parabola at the origin.

(0, 1) and (2, 5). (0, 1) and (2, 5).

An algebra slip can invent an x that never sat on the line. An algebra slip can invent an x that never sat on the line.

Negative. 1-4 is less than zero. Negative. 1-4 is less than zero.

y=2x-1. Its substituted equation has a double root. y=2x-1. Its substituted equation has a double root.